Question 1

Find the partial sum of the given sequence.
-$S _ { 5 }$ of the sequence $a _ { n } = 3 ( 4 ) ^ { n - 1 }$

Accepted Answer

A)  1023 
B)  341 
C)  63 
D)  323 
A)  1023 
B)  341 
C)  63 
D)  323

Question 2

Solve the problem.
-A triangular display of cereal boxes in a supermarket has 28 boxes in the bottom row, 25 boxes in the next row, and so on, in an arithmetic sequence. Find the general term for the sequence and how many rows there are in the display.

Accepted Answer

A)  $a _ { n } = 31 - 3 n ; 11$ rows in the display 
B)  $a _ { n } = 28 - 3 n ; 9$ rows in the display 
C)  $a _ { n } = 31 - 3 n$; 10 rows in the display 
D)  $a _ { n } = 28 - 3 n$; 8 rows in the display 
A)  $a _ { n } = 31 - 3 n ; 11$ rows in the display 
B)  $a _ { n } = 28 - 3 n ; 9$ rows in the display 
C)  $a _ { n } = 31 - 3 n$; 10 rows in the display 
D)  $a _ { n } = 28 - 3 n$; 8 rows in the display

Question 3

Solve the problem.
-A pendulum bob swings through an arc 40 inches long on its first swing. Each swing thereafter, it swings only $86 \%$ as far as on the previous swing. What is the length of the arc after 11 swings? Round your answer to two decimal places, if necessary.

Accepted Answer

A)  $7.61 \mathrm { in }$. 
B)  $344 \mathrm { in }$. 
C)  $8.85 \mathrm { in } .$ 
D)  $6.55 \mathrm { in } .$ 
A)  $7.61 \mathrm { in }$. 
B)  $344 \mathrm { in }$. 
C)  $8.85 \mathrm { in } .$ 
D)  $6.55 \mathrm { in } .$

Question 4

. Write the word or phrase that best completes each statement or answers the question.
-Suppose you just received a job offer with a starting salary of $37,000 per year and a guaranteed raise of $1500 per year. How many years will it be before you've made a total (or aggregate) salary of $1,025,000?

Accepted Answer

The answer of . Write the word or phrase that...

Question 5

Solve the problem.
-Jacie is considering a job that offers a monthly starting salary of $\$ 2500$ and guarantees her a monthly raise of $\$ 190$ during her first year on the job. Find the general term of this arithmetic sequence and her monthly salary at the end of her first year.

Accepted Answer

A)  $a _ { n } = 2500 + 190 n$; $\$ 4780$ 
B)  $a _ { n } = 2310 + 190 ( n - 1 ) ; \$ 4400$ 
C)  $a _ { n } = 2310 + 190 n ; \$ 4590$ 
D)  $a _ { n } = 2500 + 190 n ; \$ 4590$ 
A)  $a _ { n } = 2500 + 190 n$; $\$ 4780$ 
B)  $a _ { n } = 2310 + 190 ( n - 1 ) ; \$ 4400$ 
C)  $a _ { n } = 2310 + 190 n ; \$ 4590$ 
D)  $a _ { n } = 2500 + 190 n ; \$ 4590$

Question 6

Find the indicated term of the sequence.
-If the second term of a geometric progression is 45 and the third term is 9 , find $a _ { 1 }$ and $r$.

Accepted Answer

A)  $a _ { 1 } = 225 ; r = 5$ 
B)  $a _ { 1 } = \frac { 9 } { 5 } ; r = \frac { 1 } { 5 }$ 
C)  $\mathrm { a } _ { 1 } = 405 ; \mathrm { r } = \frac { 1 } { 9 }$ 
D)  $\mathrm { a } _ { 1 } = 225 ; \mathrm { r } = \frac { 1 } { 5 }$ 
A)  $a _ { 1 } = 225 ; r = 5$ 
B)  $a _ { 1 } = \frac { 9 } { 5 } ; r = \frac { 1 } { 5 }$ 
C)  $\mathrm { a } _ { 1 } = 405 ; \mathrm { r } = \frac { 1 } { 9 }$ 
D)  $\mathrm { a } _ { 1 } = 225 ; \mathrm { r } = \frac { 1 } { 5 }$

Question 7

Find a general term an for the sequence whose first four terms are given.
-$1,4,7,10 , \ldots$

Accepted Answer

A)  $a _ { n } = n + 3$ 
B)  $a _ { n } = 1 ( 3 ) ^ { n - 1 }$ 
C)  $a _ { n } = 3 n - 2$ 
D)  $a _ { n } = 2 n - 3$ 
A)  $a _ { n } = n + 3$ 
B)  $a _ { n } = 1 ( 3 ) ^ { n - 1 }$ 
C)  $a _ { n } = 3 n - 2$ 
D)  $a _ { n } = 2 n - 3$

Question 8

Solve the problem.
-To save for retirement, Sue decides to deposit $1500 into an IRA at the end of each year for the next 30 years. If the interest rate is 7% per year compounded annually, find the value of the IRA after 30
Years. Round to the nearest dollar.

Accepted Answer

A)  $2,814,804 
B)  $131,020 
C)  $141,691 
D)  $9918 
A)  $2,814,804 
B)  $131,020 
C)  $141,691 
D)  $9918

Question 9

Solve the problem.
-A theater has 22 rows with 20 seats in the first row, 23 in the second row, 26 in the third row, and so forth. How many seats are in the theater?

Accepted Answer

A)  2332 seats 
B)  1133 seats 
C)  2266 seats 
D)  1166 seats 
A)  2332 seats 
B)  1133 seats 
C)  2266 seats 
D)  1166 seats

Question 10

Solve the problem.
-Find the sum of the even integers between 37 and 69 .

Accepted Answer

A)  795 
B)  901 
C)  848 
D)  954 
A)  795 
B)  901 
C)  848 
D)  954

Question 11

Write the first five terms of the geometric sequence whose first term, a1, and common ratio, r, are given.
-$\mathrm { a } _ { 1 } = 6 ; \mathrm { r } = 5$

Accepted Answer

A)  $6,30,150,750,3750$ 
B)  $5,30,180,1080,6480$ 
C)  $30,150,750,3750,18,750$ 
D)  $6,11,16,21,26$ 
A)  $6,30,150,750,3750$ 
B)  $5,30,180,1080,6480$ 
C)  $30,150,750,3750,18,750$ 
D)  $6,11,16,21,26$

Question 12

Expand the binomial.
-$( p - q ) ^ { 6 }$

Accepted Answer

A)  $p ^ { 6 } - q ^ { 6 }$ 
B)  $\mathrm { p } ^ { 6 } - 8 \mathrm { p } ^ { 5 } \mathrm { q } + 17 \mathrm { p } ^ { 4 } \mathrm { q } ^ { 2 } - 22 \mathrm { p } ^ { 3 } \mathrm { q } ^ { 3 } + 17 \mathrm { p } ^ { 2 } \mathrm { q } ^ { 4 } - 8 \mathrm { pq } ^ { 5 } + \mathrm { q } ^ { 6 }$ 
C)  $p ^ { 6 } - 6 p ^ { 5 } q - 30 p ^ { 4 } q ^ { 2 } + 120 p ^ { 3 } q ^ { 3 } + 360 p ^ { 2 } q ^ { 4 } - 720 p q ^ { 5 } - 720 q ^ { 6 }$ 
D)  $p ^ { 6 } - 6 p ^ { 5 } q + 15 p ^ { 4 } q ^ { 2 } - 20 p ^ { 3 } q ^ { 3 } + 15 p ^ { 2 } q ^ { 4 } - 6 p q ^ { 5 } + q ^ { 6 }$ 
A)  $p ^ { 6 } - q ^ { 6 }$ 
B)  $\mathrm { p } ^ { 6 } - 8 \mathrm { p } ^ { 5 } \mathrm { q } + 17 \mathrm { p } ^ { 4 } \mathrm { q } ^ { 2 } - 22 \mathrm { p } ^ { 3 } \mathrm { q } ^ { 3 } + 17 \mathrm { p } ^ { 2 } \mathrm { q } ^ { 4 } - 8 \mathrm { pq } ^ { 5 } + \mathrm { q } ^ { 6 }$ 
C)  $p ^ { 6 } - 6 p ^ { 5 } q - 30 p ^ { 4 } q ^ { 2 } + 120 p ^ { 3 } q ^ { 3 } + 360 p ^ { 2 } q ^ { 4 } - 720 p q ^ { 5 } - 720 q ^ { 6 }$ 
D)  $p ^ { 6 } - 6 p ^ { 5 } q + 15 p ^ { 4 } q ^ { 2 } - 20 p ^ { 3 } q ^ { 3 } + 15 p ^ { 2 } q ^ { 4 } - 6 p q ^ { 5 } + q ^ { 6 }$

Question 13

Solve the problem.
-Find the sum of the first ten negative integers.

Accepted Answer

A)  $- 45$ 
B)  $- 55$ 
C)  $- 56$ 
D)  $- 66$ 
A)  $- 45$ 
B)  $- 55$ 
C)  $- 56$ 
D)  $- 66$

Question 14

Use the binomial formula to expand the binomial.
-$( 4 x - 2 ) ^ { 5 }$

Accepted Answer

A)  $1024 x ^ { 5 } - 2560 x ^ { 4 } + 2560 x ^ { 3 } - 1280 x ^ { 2 } + 320 x - 32$ 
B)  $1024 x ^ { 5 } + 320 x ^ { 4 } - 1280 x ^ { 3 } - 1280 x ^ { 2 } + 320 x - 32$ 
C)  $\left( 16 x ^ { 2 } - 16 x + 4 \right) ^ { 5 }$ 
D)  $1024 x ^ { 5 } - 512 x ^ { 4 } + 256 x ^ { 3 } - 128 x ^ { 2 } + 64 x - 32$ 
A)  $1024 x ^ { 5 } - 2560 x ^ { 4 } + 2560 x ^ { 3 } - 1280 x ^ { 2 } + 320 x - 32$ 
B)  $1024 x ^ { 5 } + 320 x ^ { 4 } - 1280 x ^ { 3 } - 1280 x ^ { 2 } + 320 x - 32$ 
C)  $\left( 16 x ^ { 2 } - 16 x + 4 \right) ^ { 5 }$ 
D)  $1024 x ^ { 5 } - 512 x ^ { 4 } + 256 x ^ { 3 } - 128 x ^ { 2 } + 64 x - 32$

Question 15

Solve the problem.
-As part of her retirement savings plan, Patricia deposited $\$ 400$ in a bank account during her first year in the workforce. During each subsequent year, she deposited $\$ 35$ more than the previous year. Find how much she deposited during her twentieth year in the workforce. Find the total amount deposited in the twenty years.

Accepted Answer

A)  $\$ 1100 ; \$ 30,000$ 
B)  $\$ 1100 ; \$ 15,000$ 
C)  $\$ 1065 ; \$ 29,300$ 
D)  $\$ 1065 ; \$ 14,650$ 
A)  $\$ 1100 ; \$ 30,000$ 
B)  $\$ 1100 ; \$ 15,000$ 
C)  $\$ 1065 ; \$ 29,300$ 
D)  $\$ 1065 ; \$ 14,650$

Question 16

Given are the first three terms of a sequence that is either arithmetic or geometric. If the sequence is arithmetic, find a1
and d. If a sequence is geometric, find a1 and r.
-$\frac { 3 } { 4 } , \frac { 3 } { 16 } , \frac { 3 } { 64 } , \ldots$

Accepted Answer

A)  $a _ { 1 } = \frac { 3 } { 4 } , r = 4$ 
B)  $a _ { 1 } = \frac { 3 } { 4 } , r = 40$ 
C)  $\mathrm { a } _ { 1 } = \frac { 3 } { 4 } , \mathrm { r } = \frac { 1 } { 40 }$ 
D)  $\mathrm { a } _ { 1 } = \frac { 3 } { 4 } , \mathrm { r } = \frac { 1 } { 4 }$ 
A)  $a _ { 1 } = \frac { 3 } { 4 } , r = 4$ 
B)  $a _ { 1 } = \frac { 3 } { 4 } , r = 40$ 
C)  $\mathrm { a } _ { 1 } = \frac { 3 } { 4 } , \mathrm { r } = \frac { 1 } { 40 }$ 
D)  $\mathrm { a } _ { 1 } = \frac { 3 } { 4 } , \mathrm { r } = \frac { 1 } { 4 }$

Question 17

Find a general term an for the sequence whose first four terms are given.
-$2,4,8,16 , \ldots$

Accepted Answer

A)  $a _ { n } = 2 + 2 ( n - 1 )$ 
B)  $a _ { n } = 2 n - 1 + 1$ 
C)  $\mathrm { a } _ { \mathrm { n } } = 2 \mathrm { n }$ 
D)  $a _ { n } = 2 n$ 
A)  $a _ { n } = 2 + 2 ( n - 1 )$ 
B)  $a _ { n } = 2 n - 1 + 1$ 
C)  $\mathrm { a } _ { \mathrm { n } } = 2 \mathrm { n }$ 
D)  $a _ { n } = 2 n$

Question 18

Find the indicated term of the sequence.
-If the fourteenth term of an arithmetic sequence is 86 and the tenth term is 62 , find the fifth term.

Accepted Answer

A)  6 
B)  32 
C)  8 
D)  38 
A)  6 
B)  32 
C)  8 
D)  38

Question 19

. Write the word or phrase that best completes each statement or answers the question.
-A local civic theater has 22 seats in the first row and 21 rows in all. Each successive row contains 3 additional seats. How many seats are in the civic theater?

Accepted Answer

A)  1070 seats 
B)  790 seats 
C)  1092 seats 
D)  1010 seats 
A)  1070 seats 
B)  790 seats 
C)  1092 seats 
D)  1010 seats

Question 20

Find the partial sum of the given sequence.
-S$_ { 20 }$ of the sequence $\mathrm { a } _ { \mathrm { n } } = - 1 + 7 ( \mathrm { n } - 1 )$

Accepted Answer

A)  1380 
B)  1310 
C)  1245 
D)  1035 
A)  1380 
B)  1310 
C)  1245 
D)  1035

Find the partial sum of the given sequence. - $S _ { 5 }$ of the sequence $a _ { n } = 3 ( 4 ) ^ { n - 1 }$

Solve the problem. -A triangular display of cereal boxes in a supermarket has 28 boxes in the bottom row, 25 boxes in the next row, and so on, in an arithmetic sequence. Find the general term for the sequence and how many rows there are in the display.

Solve the problem. -A pendulum bob swings through an arc 40 inches long on its first swing. Each swing thereafter, it swings only $86 \%$ as far as on the previous swing. What is the length of the arc after 11 swings? Round your answer to two decimal places, if necessary.

. Write the word or phrase that best completes each statement or answers the question. -Suppose you just received a job offer with a starting salary of $37,000 per year and a guaranteed raise of $1500 per year. How many years will it be before you've made a total (or aggregate) salary of $1,025,000?

Solve the problem. -Jacie is considering a job that offers a monthly starting salary of $\$ 2500$ and guarantees her a monthly raise of $\$ 190$ during her first year on the job. Find the general term of this arithmetic sequence and her monthly salary at the end of her first year.

Find the indicated term of the sequence. -If the second term of a geometric progression is 45 and the third term is 9 , find $a _ { 1 }$ and $r$ .

Find a general term an for the sequence whose first four terms are given. - $1,4,7,10 , \ldots$

Solve the problem. -To save for retirement, Sue decides to deposit $1500 into an IRA at the end of each year for the next 30 years. If the interest rate is 7% per year compounded annually, find the value of the IRA after 30 Years. Round to the nearest dollar.

Solve the problem. -A theater has 22 rows with 20 seats in the first row, 23 in the second row, 26 in the third row, and so forth. How many seats are in the theater?

Solve the problem. -Find the sum of the even integers between 37 and 69 .

Write the first five terms of the geometric sequence whose first term, a1, and common ratio, r, are given. - $\mathrm { a } _ { 1 } = 6 ; \mathrm { r } = 5$

Expand the binomial. - $( p - q ) ^ { 6 }$

Solve the problem. -Find the sum of the first ten negative integers.

Use the binomial formula to expand the binomial. - $( 4 x - 2 ) ^ { 5 }$

Given are the first three terms of a sequence that is either arithmetic or geometric. If the sequence is arithmetic, find a1 and d. If a sequence is geometric, find a1 and r. - $\frac { 3 } { 4 } , \frac { 3 } { 16 } , \frac { 3 } { 64 } , \ldots$

Find a general term an for the sequence whose first four terms are given. - $2,4,8,16 , \ldots$

Find the indicated term of the sequence. -If the fourteenth term of an arithmetic sequence is 86 and the tenth term is 62 , find the fifth term.

. Write the word or phrase that best completes each statement or answers the question. -A local civic theater has 22 seats in the first row and 21 rows in all. Each successive row contains 3 additional seats. How many seats are in the civic theater?

Find the partial sum of the given sequence. -S $_ { 20 }$ of the sequence $\mathrm { a } _ { \mathrm { n } } = - 1 + 7 ( \mathrm { n } - 1 )$

Review of Real Numbers

Equations, Inequalities, and Problem Solving

Graphing

Solving Systems of Linear Equations

Exponents and Polynomials

Factoring Polynomials

Rational Expressions

More on Functions and Graphs

Inequalities and Absolute Value

Rational Exponents, Radicals, and Complex Numbers

Quadratic Equations and Functions

Exponential and Logarithmic Functions

Conic Sections

Filters

Exam 14: Sequences, Series, and the Binomial Theorem

Find the partial sum of the given sequence. - S5S _ { 5 }S5​ of the sequence an=3(4)n−1a _ { n } = 3 ( 4 ) ^ { n - 1 }an​=3(4)n−1