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Deck 16: Series and Taylor Polynomials Web
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Question
Find the indicated term of the sequence. 
A)-44
B)47
C)49
D)-2
E)45
A)-44
B)47
C)49
D)-2
E)45
Question
Determine whether the sequence is arithmetic. If so, find the common difference. (Assume that n begins with 1.) 
A)7
B)2
C)-2
D)-7
E)not arithmetic
A)7
B)2
C)-2
D)-7
E)not arithmetic
Question
Question
Question
Write an expression for the most apparent nth term of the sequence. (Assume that 
begins with 1.) 
A)
B)
C)
D)
E)
begins with 1.) A)
B)
C)
D)
E)
Question
A deposit of $2000 is made in an account that earns 6% interest compounded monthly. The balance in the account after n months is given by 
Find the balance in the account after 11 years by finding the 132th term of the sequence. Round to the nearest penny.
A)$4,379,295.09
B)$3863.23
C)$3844.01
D)$265,320.00
E)$3882.54
Find the balance in the account after 11 years by finding the 132th term of the sequence. Round to the nearest penny.A)$4,379,295.09
B)$3863.23
C)$3844.01
D)$265,320.00
E)$3882.54
Question
Write an expression for the apparent nth term of the sequence. (Assume that n begins with 1.) 9, 12, 15, 18, 21
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Write the first five terms of the sequence. (Assume that n begins with 1.) 
A)-4, -1, 2, 5, 8
B)7, 10, 13, 16, 19
C)10, 6, 9, 12, 15
D)10, 13, 16, 19, 22
E)10, 17, 24, 31, 38
A)-4, -1, 2, 5, 8
B)7, 10, 13, 16, 19
C)10, 6, 9, 12, 15
D)10, 13, 16, 19, 22
E)10, 17, 24, 31, 38
Question
Find the fifth term of the sequence that has the given nth term. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Evaluate the series. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Suppose the ratio 
of alligators to pythons in a marshland from 2001 to 2008 can be approximated by the model 
where 
is the year, with 
corresponding to 
In 2006, the total number of alligators and pythons in the marsh was about 900. In that year, how many were pythons?
A)848
B)55
C)844
D)52
E)845
of alligators to pythons in a marshland from 2001 to 2008 can be approximated by the model where is the year, with corresponding to In 2006, the total number of alligators and pythons in the marsh was about 900. In that year, how many were pythons?A)848
B)55
C)844
D)52
E)845
Question
Match the sequence with the graph of its first 10 terms. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Write an expression for the apparent nth term of the sequence. (Assume that n begins with 1.) 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Find a formula for an for the arithmetic sequence. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Suppose that the annual payroll 
(in billions of dollars) of new car dealerships in the United States from 2000 to 2005 can be approximated by the model 
where 
represents the year, with 
corresponding to 2000. Find the total payroll from 2000 to 2005 by evaluating the sum 
Round your answer to the nearest ten million dollars.
A)$334.78 billion
B)$284.91 billion
C)$377.86 billion
D)$290.08 billion
E)$235.36 billion
(in billions of dollars) of new car dealerships in the United States from 2000 to 2005 can be approximated by the model where represents the year, with corresponding to 2000. Find the total payroll from 2000 to 2005 by evaluating the sum Round your answer to the nearest ten million dollars.A)$334.78 billion
B)$284.91 billion
C)$377.86 billion
D)$290.08 billion
E)$235.36 billion
Question
Write the given series in summation notation. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Simplify the factorial expression. 
A)2184
B)182
C)
D)14
E)2730
A)2184
B)182
C)
D)14
E)2730
Question
Find the sum. 
A)-1
B)-2
C)3
D)4
E)18
A)-1
B)-2
C)3
D)4
E)18
Question
Write the given series in summation notation. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Determine whether the sequence is arithmetic. If so, find the common difference. (Assume that n begins with 1.) 
A)-8
B)5
C)
D)8
E)not arithmetic
A)-8
B)5
C)
D)8
E)not arithmetic
Question
The annual sales 
(in millions of dollars) for a certain company from 2001 to 2006 can be approximated by the model 
where 
represents the year, with 
corresponding to 2001. Find the total sales from 2001 to 2004. Round to the nearest million.
A)$2972 million
B)$4119 million
C)$1987 million
D)$2229 million
E)$1502 million
(in millions of dollars) for a certain company from 2001 to 2006 can be approximated by the model where represents the year, with corresponding to 2001. Find the total sales from 2001 to 2004. Round to the nearest million.A)$2972 million
B)$4119 million
C)$1987 million
D)$2229 million
E)$1502 million
Question
Question
Determine whether the sequence is geometric. If so, find the common ratio. 1, -3, 9, -27, ...
A)-3
B)1
C)
D)3
E)not geometric
A)-3
B)1
C)
D)3
E)not geometric
Question
The seating section in a theater has 29 seats in the first row, 34 seats in the second row, and so on, increasing by 5 seats each row for a total of 15 rows. How many seats are in the thirteenth row?
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Use summation notation to write the sum below. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Match the arithmetic sequence with its graph from the choices below. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Find a formula for 
for the arithmetic sequence below. 
A)
B)
C)
D)
E)
for the arithmetic sequence below. A)
B)
C)
D)
E)
Question
Find the indicated nth term of the geometric sequence. 7th term: 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Determine whether the sequence is geometric. If so, find the common ratio. 5, 7, 9, 11, ...
A)2
B)5
C)
D)-2
E)not geometric
A)2
B)5
C)
D)-2
E)not geometric
Question
Question
Question
Find the partial sum. 
A)-39,339
B)-38,781
C)-39,620
D)-39,903
E)-39,340
A)-39,339
B)-38,781
C)-39,620
D)-39,903
E)-39,340
Question
Match the geometric sequence with its graph from the choices below. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Use a graphing utility to graph the first 10 terms of the sequence. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Find the nth term of the geometric sequence. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Write the first five terms of the arithmetic sequence. 
A)-5, -11, -17, -23, -29
B)1, 7, 13, 19, 25
C)-5, 1, 7, 13, 19
D)-5, -30, -180, -1080, -6480
E)-5, 1, -4, -9, -14
A)-5, -11, -17, -23, -29
B)1, 7, 13, 19, 25
C)-5, 1, 7, 13, 19
D)-5, -30, -180, -1080, -6480
E)-5, 1, -4, -9, -14
Question
Write the first five terms of the geometric sequence. 
A)-1, -7, -13, -19, -25
B)-1, 6, -36, 216, -1296
C)
D)
E)
A)-1, -7, -13, -19, -25
B)-1, 6, -36, 216, -1296
C)
D)
E)
Question
Find the nth term of the geometric sequence. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Question
Question
Write an expression for the nth term of the sequence 
.
A)
B)
C)
D)
E)
.A)
B)
C)
D)
E)
Question
Find the sum of the finite geometric series. Round to the nearest hundredth. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Find the rational number representation of the repeating decimal. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Write the first five terms of the sequence. an = 
A)
B)
C)
D)
E)none of the above
A)
B)
C)
D)
E)none of the above
Question
Determine the convergence or divergence of the sequence 
. If the sequence converges, use a symbolic algebra utility to find its limit.
A)9
B)4
C)5
D)
E)The sequence diverges.
. If the sequence converges, use a symbolic algebra utility to find its limit.A)9
B)4
C)5
D)
E)The sequence diverges.
Question
Find the sum of the finite geometric series. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Use summation notation to write the sum. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Write an expression for the nth term of the sequence 2, 8, 26, 80, ....
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Find the limit of the sequence 
.
A)
B)
C)
D)
E)The sequence diverges.
.A)
B)
C)
D)
E)The sequence diverges.
Question
Write the first five terms of the sequence. an = 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Find the limit of the following sequence. 
A)
B)
C)
D)
E)The sequence diverges.
A)
B)
C)
D)
E)The sequence diverges.
Question
Find the sum of the finite geometric sequence. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Find the limit of the following sequence. 
A)3
B)1
C)
D)-3
E)The sequence diverges.
A)3
B)1
C)
D)-3
E)The sequence diverges.
Question
The annual profit 
(in millions of dollars) for a certain company from 2000 to 2005 can be approximated by the model 
where 
represents the year, with 
corresponding to 2000. Use the formula for the sum of a finite geometric sequence to approximate the total profit earned during this six-year period. Round to the nearest ten-thousand dollars.
A)$3810.36 million
B)$4112.94 million
C)$3132.16 million
D)$2829.58 million
E)$2325.95 million
(in millions of dollars) for a certain company from 2000 to 2005 can be approximated by the model where represents the year, with corresponding to 2000. Use the formula for the sum of a finite geometric sequence to approximate the total profit earned during this six-year period. Round to the nearest ten-thousand dollars.A)$3810.36 million
B)$4112.94 million
C)$3132.16 million
D)$2829.58 million
E)$2325.95 million
Question
Write the rational number 
as the quotient of two integers in simplest form.
A)
B)
C)
D)
E)
as the quotient of two integers in simplest form.A)
B)
C)
D)
E)
Question
Find the sum of the infinite geometric series. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Write an expression for the nth term of the sequence. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Find the sum of the infinite geometric series below. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Find the sum of the infinite geometric series. 
A)
B)
C)
D)
E)undefined
A)
B)
C)
D)
E)undefined
Question
Find the limit of the following sequence. 
A)
B)1
C)2
D)
E)The sequence diverges.
A)
B)1
C)2
D)
E)The sequence diverges.
Question
The repeating decimal 
is expressed as a geometric series 
. Write the decimal 
as the ratio of two integers.
A)
B)
C)
D)
E)
is expressed as a geometric series . Write the decimal as the ratio of two integers.A)
B)
C)
D)
E)
Question
A deposit of 
200 is made each month in an account that earns 8.4% interest, compounded monthly. The balance in the account after n months is given by 
. Find the balance after 22 years by computing the 264th term of the sequence. Round your answer to two decimal places.
A)$213,316.53
B)$293,716.53
C)$6,667.78
D)$86,634.61
E)$281.40
200 is made each month in an account that earns 8.4% interest, compounded monthly. The balance in the account after n months is given by . Find the balance after 22 years by computing the 264th term of the sequence. Round your answer to two decimal places.A)$213,316.53
B)$293,716.53
C)$6,667.78
D)$86,634.61
E)$281.40
Question
A ball is dropped from a height of 14 feet, and on each rebound it rises to 
its preceding height. Write an expression for the height of the nth rebound.
A)
B)
C)
D)
E)
its preceding height. Write an expression for the height of the nth rebound.A)
B)
C)
D)
E)
Question
Find the sum of the convergent series. 
A)
B)
C)
D)9
E)8
A)
B)
C)
D)9
E)8
Question
Determine the convergence or divergence of the following series. Use a symbolic algebra utility to verify your result. 
A)The series diverges.
B)The series converges.
A)The series diverges.
B)The series converges.
Question
Determine whether the series 
is a p-series.
A)
is not a 
series.
B)
is a 
series.
is a p-series.A)
is not a series.B)
is a series. Question
What are the next three terms in the arithmetic sequence 
?
A)
B)
C)
D)
E)
?A)
B)
C)
D)
E)
Question
Determine the convergence or divergence of the series 
. Use a symbolic algebra utility to verify your result.
A)The series converges.
B)The series diverges.
. Use a symbolic algebra utility to verify your result.A)The series converges.
B)The series diverges.
Question
Determine the convergence or divergence of the series 
. Use a symbolic algebra utility to verify your result.
A)The series converges.
B)The series diverges.
. Use a symbolic algebra utility to verify your result.A)The series converges.
B)The series diverges.
Question
Find the next three terms of the geometric sequence. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Express the value of the given repeating decimal as a fraction. [Hint: Write as an infinite series.] ![<strong>Express the value of the given repeating decimal as a fraction. [Hint: Write as an infinite series.] </strong> A) B) C) D) E) <div style=padding-top: 35px>](https://storage.examlex.com/TB8692/11eb99ec_11c7_5600_bdc5_53df09d9f5a4_TB8692_11.jpg)
A)![<strong>Express the value of the given repeating decimal as a fraction. [Hint: Write as an infinite series.] </strong> A) B) C) D) E) <div style=padding-top: 35px>](https://storage.examlex.com/TB8692/11eb99ec_11c7_5601_bdc5_194a410f17c6_TB8692_11.jpg)
B)![<strong>Express the value of the given repeating decimal as a fraction. [Hint: Write as an infinite series.] </strong> A) B) C) D) E) <div style=padding-top: 35px>](https://storage.examlex.com/TB8692/11eb99ec_11c7_5602_bdc5_dd4a3b34255c_TB8692_11.jpg)
C)![<strong>Express the value of the given repeating decimal as a fraction. [Hint: Write as an infinite series.] </strong> A) B) C) D) E) <div style=padding-top: 35px>](https://storage.examlex.com/TB8692/11eb99ec_11c7_5603_bdc5_517aec4b4854_TB8692_11.jpg)
D)![<strong>Express the value of the given repeating decimal as a fraction. [Hint: Write as an infinite series.] </strong> A) B) C) D) E) <div style=padding-top: 35px>](https://storage.examlex.com/TB8692/11eb99ec_11c7_5604_bdc5_0f1d9bdbb277_TB8692_11.jpg)
E)![<strong>Express the value of the given repeating decimal as a fraction. [Hint: Write as an infinite series.] </strong> A) B) C) D) E) <div style=padding-top: 35px>](https://storage.examlex.com/TB8692/11eb99ec_11c7_5605_bdc5_97ba3f0800ad_TB8692_11.jpg)
A)
B)
C)
D)
E)
Question
Write the first five terms of the sequence of partial sums. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
The annual spending by tourists in a resort city is 200 million dollars. Approximately 75% of that revenue is again spent in the resort city, and of that amount approximately 75% is again spent in the resort city. If this pattern continues, write the geometric series that gives the total amount of spending generated by the 200 million dollars (including the initial outlay of 200 million dollars) and find the sum of the series.
A)The geometric series is
.The sum of the series is 
800.00 million.
B)The geometric series is
.The sum of the series is 
15,000 million.
C)The geometric series is
.The sum of the series is 
800.00 million.
D)The geometric series is
.The sum of the series is 
15,000 million.
E)The geometric series is
.The sum of the series is 
150.00 million.
A)The geometric series is
.The sum of the series is 800.00 million.B)The geometric series is
.The sum of the series is 15,000 million.C)The geometric series is
.The sum of the series is 800.00 million.D)The geometric series is
.The sum of the series is 15,000 million.E)The geometric series is
.The sum of the series is 150.00 million. Question
You accept a job that pays a salary of 
50,000 the first year. During the next 39 years, you will receive a 4% raise each year. What would be your total compensation over the 40-year period? Round your answer to the nearest integer.
A)
4,751,276
B)
1,250,000
C)
48,000
D)
200,000
E)
2,000
50,000 the first year. During the next 39 years, you will receive a 4% raise each year. What would be your total compensation over the 40-year period? Round your answer to the nearest integer.A)
4,751,276B)
1,250,000C)
48,000D)
200,000E)
2,000 Question
Consider the sequence (An) whose nth term is given by An 
where P is the principal, An is the amount of compound interest after n months, and r is the annual percentage rate. Write the first four terms of the sequence for P = 
8,000 and r = 0.04. Round your answer to two decimal places.
A)8026.67, 8063.49, 8101.43, 8107.20
B)8027.67, 8063.49, 8101.43, 8135.19
C)8026.67, 8053.42, 8080.27, 8107.20
D)8027.67, 8063.49, 8080.27, 8107.20
E)8027.67, 8053.42, 8080.27, 8135.19
where P is the principal, An is the amount of compound interest after n months, and r is the annual percentage rate. Write the first four terms of the sequence for P = 8,000 and r = 0.04. Round your answer to two decimal places.A)8026.67, 8063.49, 8101.43, 8107.20
B)8027.67, 8063.49, 8101.43, 8135.19
C)8026.67, 8053.42, 8080.27, 8107.20
D)8027.67, 8063.49, 8080.27, 8107.20
E)8027.67, 8053.42, 8080.27, 8135.19
Question
Question
Find the sum of the convergent series. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
A company produces a new product for which it estimates the annual sales to be 5000 units. Suppose that in any given year 
% of the units (regardless of age) will become inoperative. How many units will be in use after n years?
A)
B)
C)
D)
E)
% of the units (regardless of age) will become inoperative. How many units will be in use after n years?A)
B)
C)
D)
E)
Question
Give an example of a sequence that converges to 
.
A)
B)
C)
D)
E)
.A)
B)
C)
D)
E)
Question
Bouncing Ball. A ball dropped from a height of 35 feet bounces to 
of its former height with each bounce. Find the total vertical distance that the ball travels.
A)105 feet
B)140 feet
C)64 feet
D)53 feet
E)70 feet
of its former height with each bounce. Find the total vertical distance that the ball travels.A)105 feet
B)140 feet
C)64 feet
D)53 feet
E)70 feet
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Deck 16: Series and Taylor Polynomials Web
1
Find the indicated term of the sequence.
A)-44
B)47
C)49
D)-2
E)45
A)-44
B)47
C)49
D)-2
E)45
47
2
Determine whether the sequence is arithmetic. If so, find the common difference. (Assume that n begins with 1.)
A)7
B)2
C)-2
D)-7
E)not arithmetic
A)7
B)2
C)-2
D)-7
E)not arithmetic
-7
3
Determine whether the sequence is arithmetic. If so, find the common difference. 2, 1, 0, -1, -2
A)3
B)-1
C)2
D)1
E)not arithmetic
A)3
B)-1
C)2
D)1
E)not arithmetic
-1
4
Determine whether the sequence is arithmetic. If so, find the common difference. 3, 9, 27, 81, 243
A)3
B)3n
C)3n - 3n-1
D)-3
E)not arithmetic
A)3
B)3n
C)3n - 3n-1
D)-3
E)not arithmetic
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5
Write an expression for the most apparent nth term of the sequence. (Assume that begins with 1.)
A)
B)
C)
D)
E)
begins with 1.) A)
B)
C)
D)
E)
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6
A deposit of $2000 is made in an account that earns 6% interest compounded monthly. The balance in the account after n months is given by Find the balance in the account after 11 years by finding the 132th term of the sequence. Round to the nearest penny.
A)$4,379,295.09
B)$3863.23
C)$3844.01
D)$265,320.00
E)$3882.54
Find the balance in the account after 11 years by finding the 132th term of the sequence. Round to the nearest penny.A)$4,379,295.09
B)$3863.23
C)$3844.01
D)$265,320.00
E)$3882.54
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7
Write an expression for the apparent nth term of the sequence. (Assume that n begins with 1.) 9, 12, 15, 18, 21
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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8
Write the first five terms of the sequence. (Assume that n begins with 1.)
A)-4, -1, 2, 5, 8
B)7, 10, 13, 16, 19
C)10, 6, 9, 12, 15
D)10, 13, 16, 19, 22
E)10, 17, 24, 31, 38
A)-4, -1, 2, 5, 8
B)7, 10, 13, 16, 19
C)10, 6, 9, 12, 15
D)10, 13, 16, 19, 22
E)10, 17, 24, 31, 38
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9
Find the fifth term of the sequence that has the given nth term.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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10
Evaluate the series.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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11
Suppose the ratio of alligators to pythons in a marshland from 2001 to 2008 can be approximated by the model where is the year, with corresponding to In 2006, the total number of alligators and pythons in the marsh was about 900. In that year, how many were pythons?
A)848
B)55
C)844
D)52
E)845
of alligators to pythons in a marshland from 2001 to 2008 can be approximated by the model where is the year, with corresponding to In 2006, the total number of alligators and pythons in the marsh was about 900. In that year, how many were pythons?A)848
B)55
C)844
D)52
E)845
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k this deck
12
Match the sequence with the graph of its first 10 terms.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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k this deck
13
Write an expression for the apparent nth term of the sequence. (Assume that n begins with 1.)
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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k this deck
14
Find a formula for an for the arithmetic sequence.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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k this deck
15
Suppose that the annual payroll (in billions of dollars) of new car dealerships in the United States from 2000 to 2005 can be approximated by the model where represents the year, with corresponding to 2000. Find the total payroll from 2000 to 2005 by evaluating the sum Round your answer to the nearest ten million dollars.
A)$334.78 billion
B)$284.91 billion
C)$377.86 billion
D)$290.08 billion
E)$235.36 billion
(in billions of dollars) of new car dealerships in the United States from 2000 to 2005 can be approximated by the model where represents the year, with corresponding to 2000. Find the total payroll from 2000 to 2005 by evaluating the sum Round your answer to the nearest ten million dollars.A)$334.78 billion
B)$284.91 billion
C)$377.86 billion
D)$290.08 billion
E)$235.36 billion
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16
Write the given series in summation notation.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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k this deck
17
Simplify the factorial expression.
A)2184
B)182
C)
D)14
E)2730
A)2184
B)182
C)
D)14
E)2730
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18
Find the sum.
A)-1
B)-2
C)3
D)4
E)18
A)-1
B)-2
C)3
D)4
E)18
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19
Write the given series in summation notation.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Unlock Deck
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20
Determine whether the sequence is arithmetic. If so, find the common difference. (Assume that n begins with 1.)
A)-8
B)5
C)
D)8
E)not arithmetic
A)-8
B)5
C)
D)8
E)not arithmetic
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k this deck
21
The annual sales (in millions of dollars) for a certain company from 2001 to 2006 can be approximated by the model where represents the year, with corresponding to 2001. Find the total sales from 2001 to 2004. Round to the nearest million.
A)$2972 million
B)$4119 million
C)$1987 million
D)$2229 million
E)$1502 million
(in millions of dollars) for a certain company from 2001 to 2006 can be approximated by the model where represents the year, with corresponding to 2001. Find the total sales from 2001 to 2004. Round to the nearest million.A)$2972 million
B)$4119 million
C)$1987 million
D)$2229 million
E)$1502 million
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22
Find the sum of the integers from 5 to 27.
A)378
B)22
C)736
D)368
E)756
A)378
B)22
C)736
D)368
E)756
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23
Determine whether the sequence is geometric. If so, find the common ratio. 1, -3, 9, -27, ...
A)-3
B)1
C)
D)3
E)not geometric
A)-3
B)1
C)
D)3
E)not geometric
Unlock Deck
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24
The seating section in a theater has 29 seats in the first row, 34 seats in the second row, and so on, increasing by 5 seats each row for a total of 15 rows. How many seats are in the thirteenth row?
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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25
Use summation notation to write the sum below.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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26
Match the arithmetic sequence with its graph from the choices below.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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k this deck
27
Find a formula for for the arithmetic sequence below.
A)
B)
C)
D)
E)
for the arithmetic sequence below. A)
B)
C)
D)
E)
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28
Find the indicated nth term of the geometric sequence. 7th term:
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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29
Determine whether the sequence is geometric. If so, find the common ratio. 5, 7, 9, 11, ...
A)2
B)5
C)
D)-2
E)not geometric
A)2
B)5
C)
D)-2
E)not geometric
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30
Find the indicated nth partial sum of the arithmetic sequence. 3.4, 6.2, 9, 11.8, ..., n = 10
A)181
B)188
C)160
D)159.4
E)160.6
A)181
B)188
C)160
D)159.4
E)160.6
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31
A heavy object (with negligible air resistance) is dropped from a plane. During the first second of fall, the object falls 17.4 meters; during the second second, it falls 52.2 meters; during the third second, it falls 87.0 meters; and during the fourth second, it falls 121.8 meters. If this pattern continues, how many meters will the object fall in 10 seconds?
A)2505.6 meters
B)1409.4 meters
C)626.4 meters
D)1740.0 meters
E)852.6 meters
A)2505.6 meters
B)1409.4 meters
C)626.4 meters
D)1740.0 meters
E)852.6 meters
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32
Find the partial sum.
A)-39,339
B)-38,781
C)-39,620
D)-39,903
E)-39,340
A)-39,339
B)-38,781
C)-39,620
D)-39,903
E)-39,340
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33
Match the geometric sequence with its graph from the choices below.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Unlock Deck
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34
Use a graphing utility to graph the first 10 terms of the sequence.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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35
Find the nth term of the geometric sequence.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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36
Write the first five terms of the arithmetic sequence.
A)-5, -11, -17, -23, -29
B)1, 7, 13, 19, 25
C)-5, 1, 7, 13, 19
D)-5, -30, -180, -1080, -6480
E)-5, 1, -4, -9, -14
A)-5, -11, -17, -23, -29
B)1, 7, 13, 19, 25
C)-5, 1, 7, 13, 19
D)-5, -30, -180, -1080, -6480
E)-5, 1, -4, -9, -14
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37
Write the first five terms of the geometric sequence.
A)-1, -7, -13, -19, -25
B)-1, 6, -36, 216, -1296
C)
D)
E)
A)-1, -7, -13, -19, -25
B)-1, 6, -36, 216, -1296
C)
D)
E)
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38
Find the nth term of the geometric sequence.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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39
Logs are stacked so that there are 17 logs in the bottom row, 16 logs in the second row from the bottom, and so on, decreasing by 1 log each row. How many logs are there in the first five rows from the bottom?
A)117 logs
B)108 logs
C)75 logs
D)87 logs
E)125 logs
A)117 logs
B)108 logs
C)75 logs
D)87 logs
E)125 logs
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40
Consider a job offer with a starting salary of $43,200 and a given annual raise of $2175. Determine the total compensation from the company through seven full years of employment.
A)$406,500
B)$291,825
C)$185,850
D)$136,125
E)$348,075
A)$406,500
B)$291,825
C)$185,850
D)$136,125
E)$348,075
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41
Write an expression for the nth term of the sequence .
A)
B)
C)
D)
E)
.A)
B)
C)
D)
E)
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42
Find the sum of the finite geometric series. Round to the nearest hundredth.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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43
Find the rational number representation of the repeating decimal.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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k this deck
44
Write the first five terms of the sequence. an =
A)
B)
C)
D)
E)none of the above
A)
B)
C)
D)
E)none of the above
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k this deck
45
Determine the convergence or divergence of the sequence . If the sequence converges, use a symbolic algebra utility to find its limit.
A)9
B)4
C)5
D)
E)The sequence diverges.
. If the sequence converges, use a symbolic algebra utility to find its limit.A)9
B)4
C)5
D)
E)The sequence diverges.
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46
Find the sum of the finite geometric series.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Unlock Deck
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k this deck
47
Use summation notation to write the sum.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Unlock Deck
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k this deck
48
Write an expression for the nth term of the sequence 2, 8, 26, 80, ....
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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k this deck
49
Find the limit of the sequence .
A)
B)
C)
D)
E)The sequence diverges.
.A)
B)
C)
D)
E)The sequence diverges.
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50
Write the first five terms of the sequence. an =
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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k this deck
51
Find the limit of the following sequence.
A)
B)
C)
D)
E)The sequence diverges.
A)
B)
C)
D)
E)The sequence diverges.
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52
Find the sum of the finite geometric sequence.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Unlock Deck
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k this deck
53
Find the limit of the following sequence.
A)3
B)1
C)
D)-3
E)The sequence diverges.
A)3
B)1
C)
D)-3
E)The sequence diverges.
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54
The annual profit (in millions of dollars) for a certain company from 2000 to 2005 can be approximated by the model where represents the year, with corresponding to 2000. Use the formula for the sum of a finite geometric sequence to approximate the total profit earned during this six-year period. Round to the nearest ten-thousand dollars.
A)$3810.36 million
B)$4112.94 million
C)$3132.16 million
D)$2829.58 million
E)$2325.95 million
(in millions of dollars) for a certain company from 2000 to 2005 can be approximated by the model where represents the year, with corresponding to 2000. Use the formula for the sum of a finite geometric sequence to approximate the total profit earned during this six-year period. Round to the nearest ten-thousand dollars.A)$3810.36 million
B)$4112.94 million
C)$3132.16 million
D)$2829.58 million
E)$2325.95 million
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55
Write the rational number as the quotient of two integers in simplest form.
A)
B)
C)
D)
E)
as the quotient of two integers in simplest form.A)
B)
C)
D)
E)
Unlock Deck
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56
Find the sum of the infinite geometric series.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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57
Write an expression for the nth term of the sequence.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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58
Find the sum of the infinite geometric series below.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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59
Find the sum of the infinite geometric series.
A)
B)
C)
D)
E)undefined
A)
B)
C)
D)
E)undefined
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k this deck
60
Find the limit of the following sequence.
A)
B)1
C)2
D)
E)The sequence diverges.
A)
B)1
C)2
D)
E)The sequence diverges.
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k this deck
61
The repeating decimal is expressed as a geometric series . Write the decimal as the ratio of two integers.
A)
B)
C)
D)
E)
is expressed as a geometric series . Write the decimal as the ratio of two integers.A)
B)
C)
D)
E)
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62
A deposit of 200 is made each month in an account that earns 8.4% interest, compounded monthly. The balance in the account after n months is given by . Find the balance after 22 years by computing the 264th term of the sequence. Round your answer to two decimal places.
A)$213,316.53
B)$293,716.53
C)$6,667.78
D)$86,634.61
E)$281.40
200 is made each month in an account that earns 8.4% interest, compounded monthly. The balance in the account after n months is given by . Find the balance after 22 years by computing the 264th term of the sequence. Round your answer to two decimal places.A)$213,316.53
B)$293,716.53
C)$6,667.78
D)$86,634.61
E)$281.40
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63
A ball is dropped from a height of 14 feet, and on each rebound it rises to its preceding height. Write an expression for the height of the nth rebound.
A)
B)
C)
D)
E)
its preceding height. Write an expression for the height of the nth rebound.A)
B)
C)
D)
E)
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64
Find the sum of the convergent series.
A)
B)
C)
D)9
E)8
A)
B)
C)
D)9
E)8
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65
Determine the convergence or divergence of the following series. Use a symbolic algebra utility to verify your result.
A)The series diverges.
B)The series converges.
A)The series diverges.
B)The series converges.
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66
Determine whether the series is a p-series.
A) is not a series.
B) is a series.
is a p-series.A)
is not a series.B)
is a series. Unlock Deck
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67
What are the next three terms in the arithmetic sequence ?
A)
B)
C)
D)
E)
?A)
B)
C)
D)
E)
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k this deck
68
Determine the convergence or divergence of the series . Use a symbolic algebra utility to verify your result.
A)The series converges.
B)The series diverges.
. Use a symbolic algebra utility to verify your result.A)The series converges.
B)The series diverges.
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69
Determine the convergence or divergence of the series . Use a symbolic algebra utility to verify your result.
A)The series converges.
B)The series diverges.
. Use a symbolic algebra utility to verify your result.A)The series converges.
B)The series diverges.
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70
Find the next three terms of the geometric sequence.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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71
Express the value of the given repeating decimal as a fraction. [Hint: Write as an infinite series.]
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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72
Write the first five terms of the sequence of partial sums.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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k this deck
73
The annual spending by tourists in a resort city is 200 million dollars. Approximately 75% of that revenue is again spent in the resort city, and of that amount approximately 75% is again spent in the resort city. If this pattern continues, write the geometric series that gives the total amount of spending generated by the 200 million dollars (including the initial outlay of 200 million dollars) and find the sum of the series.
A)The geometric series is .The sum of the series is 800.00 million.
B)The geometric series is .The sum of the series is 15,000 million.
C)The geometric series is .The sum of the series is 800.00 million.
D)The geometric series is .The sum of the series is 15,000 million.
E)The geometric series is .The sum of the series is 150.00 million.
A)The geometric series is
.The sum of the series is 800.00 million.B)The geometric series is
.The sum of the series is 15,000 million.C)The geometric series is
.The sum of the series is 800.00 million.D)The geometric series is
.The sum of the series is 15,000 million.E)The geometric series is
.The sum of the series is 150.00 million. Unlock Deck
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74
You accept a job that pays a salary of 50,000 the first year. During the next 39 years, you will receive a 4% raise each year. What would be your total compensation over the 40-year period? Round your answer to the nearest integer.
A) 4,751,276
B) 1,250,000
C) 48,000
D) 200,000
E) 2,000
50,000 the first year. During the next 39 years, you will receive a 4% raise each year. What would be your total compensation over the 40-year period? Round your answer to the nearest integer.A)
4,751,276B)
1,250,000C)
48,000D)
200,000E)
2,000 Unlock Deck
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75
Consider the sequence (An) whose nth term is given by An where P is the principal, An is the amount of compound interest after n months, and r is the annual percentage rate. Write the first four terms of the sequence for P = 8,000 and r = 0.04. Round your answer to two decimal places.
A)8026.67, 8063.49, 8101.43, 8107.20
B)8027.67, 8063.49, 8101.43, 8135.19
C)8026.67, 8053.42, 8080.27, 8107.20
D)8027.67, 8063.49, 8080.27, 8107.20
E)8027.67, 8053.42, 8080.27, 8135.19
where P is the principal, An is the amount of compound interest after n months, and r is the annual percentage rate. Write the first four terms of the sequence for P = 8,000 and r = 0.04. Round your answer to two decimal places.A)8026.67, 8063.49, 8101.43, 8107.20
B)8027.67, 8063.49, 8101.43, 8135.19
C)8026.67, 8053.42, 8080.27, 8107.20
D)8027.67, 8063.49, 8080.27, 8107.20
E)8027.67, 8053.42, 8080.27, 8135.19
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76
A factory is polluting a river such that at every mile down river from the factory an environmental expert finds 20% less pollutant than at the preceding mile. If the pollutant's concentration is 700 ppm (parts per million) at the factory, what is its concentration 15 miles down river?
A)140.00 ppm
B)300.00 ppm
C)24.63 ppm
D)875.00 ppm
E)30.79 ppm
A)140.00 ppm
B)300.00 ppm
C)24.63 ppm
D)875.00 ppm
E)30.79 ppm
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77
Find the sum of the convergent series.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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k this deck
78
A company produces a new product for which it estimates the annual sales to be 5000 units. Suppose that in any given year % of the units (regardless of age) will become inoperative. How many units will be in use after n years?
A)
B)
C)
D)
E)
% of the units (regardless of age) will become inoperative. How many units will be in use after n years?A)
B)
C)
D)
E)
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79
Give an example of a sequence that converges to .
A)
B)
C)
D)
E)
.A)
B)
C)
D)
E)
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80
Bouncing Ball. A ball dropped from a height of 35 feet bounces to of its former height with each bounce. Find the total vertical distance that the ball travels.
A)105 feet
B)140 feet
C)64 feet
D)53 feet
E)70 feet
of its former height with each bounce. Find the total vertical distance that the ball travels.A)105 feet
B)140 feet
C)64 feet
D)53 feet
E)70 feet
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Unlock for access to all 127 flashcards in this deck.
Unlock Deck
k this deck
Unlock Deck
Unlock for access to all 127 flashcards in this deck.
