Question 1

Solve the problem.
-$$\text { Find the } 10 \text { th term of the geometric sequence } \frac { 1 } { 3 } , 1,3 , \ldots$$

Accepted Answer

A)  2187 
B)  177,147 
C)  19683 
D)  6561 
A)  2187 
B)  177,147 
C)  19683 
D)  6561

Question 2

Find the indicated term using the given information.
-$5,2 , - 1 , \ldots ;$ a 44

Accepted Answer

A)  134 
B)  $- 127$ 
C)  137 
D)  $- 124$ 
A)  134 
B)  $- 127$ 
C)  137 
D)  $- 124$

Question 3

Find the indicated term using the given information.
-$$\mathrm { a } _ { 45 } = - \frac { 147 } { 5 } , \mathrm { a } _ { 13 } = - \frac { 51 } { 5 } ; \mathrm { a } _ { 3 }$$

Accepted Answer

A)  $- \frac { 21 } { 5 }$ 
B)  15 
C)  $- \frac { 24 } { 5 }$ 
D)  $- \frac { 3 } { 5 }$ 
A)  $- \frac { 21 } { 5 }$ 
B)  15 
C)  $- \frac { 24 } { 5 }$ 
D)  $- \frac { 3 } { 5 }$

Question 4

Write the word or phrase that best completes each statement or answers the question.
-For the geometric sequence 64, 16, 4, 1, ... , find an.

Accepted Answer

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

Question 5

If the sequence is geometric, find the common ratio. If the sequence is not geometric, say so.
-$$\frac { 3 } { 4 } , \frac { 3 } { 16 } , \frac { 3 } { 64 } , \frac { 3 } { 256 } , \frac { 3 } { 1,024 }$$

Accepted Answer

A)  $\frac { 1 } { 4 }$ 
B)  4 
C)  40 
D)  $\frac { 1 } { 40 }$ 
A)  $\frac { 1 } { 4 }$ 
B)  4 
C)  40 
D)  $\frac { 1 } { 40 }$

Question 6

Use the formula for the general term (the nth term) of a geometric sequence to find the indicated term of the sequence
with the given first term, a1, and common ratio, r.
-Find a9 when a1 = 2, r = -2.

Accepted Answer

A)  -14 
B)  512 
C)  -1,024 
D)  516 
A)  -14 
B)  512 
C)  -1,024 
D)  516

Question 7

Choose the one alternative that best completes the statement or answers the question.
Evaluate the expression.
-$\left( \begin{array} { l } 6 \ 0 \end{array} \right)$

Accepted Answer

A)  1 
B)  0 
C)  720 
D)  2 
A)  1 
B)  0 
C)  720 
D)  2

Question 8

Use the formula for the general term (the nth term) of a geometric sequence to find the indicated term of the sequence
with the given first term, a1, and common ratio, r.
-Find ag when $a _ { 1 } = 50,000 , r = 0.1$.

Accepted Answer

A)  $0.00005$ 
B)  $0.0005$ 
C)  $50,000.8$ 
D)  $0.000005$ 
A)  $0.00005$ 
B)  $0.0005$ 
C)  $50,000.8$ 
D)  $0.000005$

Question 9

Solve the problem.
-Suppose that certain bacteria can double their size and divide every 30 minutes. Write a recursive sequence that describes this growth where each value of $\mathrm { n }$ represents a 30 -minute interval. Let a $1 = 490$ represent the initial number of bacteria present.

Accepted Answer

A)  $a _ { n } = 2 a _ { 1 }$ for all values of $n$. 
B)  $a _ { 1 } = 490 ; \quad a _ { n } = 2 a _ { n } + 1$ for $n > 1$ 
C)  $\mathrm { a } _ { 1 } = 490 ; \mathrm { a } _ { \mathrm { n } } = 2 \mathrm { a } _ { \mathrm { n } - 1 }$ for $\mathrm { n } > 1$. 
D)  $a _ { 1 } = 490 ; \quad a _ { n } = \frac { 1 } { 2 } a _ { n - 1 } \quad$ for $n > 1$ 
A)  $a _ { n } = 2 a _ { 1 }$ for all values of $n$. 
B)  $a _ { 1 } = 490 ; \quad a _ { n } = 2 a _ { n } + 1$ for $n > 1$ 
C)  $\mathrm { a } _ { 1 } = 490 ; \mathrm { a } _ { \mathrm { n } } = 2 \mathrm { a } _ { \mathrm { n } - 1 }$ for $\mathrm { n } > 1$. 
D)  $a _ { 1 } = 490 ; \quad a _ { n } = \frac { 1 } { 2 } a _ { n - 1 } \quad$ for $n > 1$

Question 10

Solve the problem.
-The population of a town is increasing by 300 inhabitants each year. If its population at the beginning of 1990 was 26,587, what was its population at the beginning of 1996?

Accepted Answer

A)  318,954 inhabitants 
B)  159,477 inhabitants 
C)  28,087 inhabitants 
D)  28,387 inhabitants 
A)  318,954 inhabitants 
B)  159,477 inhabitants 
C)  28,087 inhabitants 
D)  28,387 inhabitants

Question 11

Determine whether the infinite geometric series converges or diverges. If it converges, find its sum.
-$$20 + 10 + 5 + \cdots$$

Accepted Answer

A)  Converges; 40 
B)  Converges; 20 
C)  Converges; $- 20$ 
D)  Converges; 35 
A)  Converges; 40 
B)  Converges; 20 
C)  Converges; $- 20$ 
D)  Converges; 35

Question 12

Express the sum using summation notation.
-$$\frac { 5 ^ { 14 } } { 9 ^ { 4 } } + \frac { 5 ^ { 13 } } { 9 ^ { 5 } } + \frac { 5 ^ { 12 } } { 9 ^ { 6 } } + \ldots + \frac { 5 ^ { 7 } } { 9 ^ { 11 } }$$

Accepted Answer

A)  $\sum _ { k = 1 } ^ { 4 } \frac { 5 ^ { 15 + k } } { 9 ^ { 3 + k } }$ 
B)  $\sum _ { k = 1 } ^ { 8 } \frac { 5 ^ { - k } } { 9 ^ { 3 + k } }$ 
C)  $\sum _ { k = 1 } ^ { 8 } \frac { 5 ^ { 15 - k } } { 9 ^ { k } }$ 
D)  $\sum _ { k = 1 } ^ { 8 } \frac { 5 ^ { 15 - k } } { 9 ^ { 3 + k } }$ 
A)  $\sum _ { k = 1 } ^ { 4 } \frac { 5 ^ { 15 + k } } { 9 ^ { 3 + k } }$ 
B)  $\sum _ { k = 1 } ^ { 8 } \frac { 5 ^ { - k } } { 9 ^ { 3 + k } }$ 
C)  $\sum _ { k = 1 } ^ { 8 } \frac { 5 ^ { 15 - k } } { 9 ^ { k } }$ 
D)  $\sum _ { k = 1 } ^ { 8 } \frac { 5 ^ { 15 - k } } { 9 ^ { 3 + k } }$

Question 13

Use a graphing utility to find the sum of the geometric sequence. Round answer to two decimal places, if necessary.
-$$\sum _ { k = 1 } ^ { 12 } \frac { 1 } { 7 } \cdot ( - 2 ) ^ { \mathrm { k } - 1 }$$

Accepted Answer

A)  $- 195$ 
B)  -195.86 
C)  $- 194$ 
D)  $- 195.29$ 
A)  $- 195$ 
B)  -195.86 
C)  $- 194$ 
D)  $- 195.29$

Question 14

Use the formula for the general term (the nth term) of a geometric sequence to find the indicated term of the sequence
with the given first term, a1, and common ratio, r.
-Find a7 for the sequence 0.7, 0.07, 0.007, . . .

Accepted Answer

A)  0.00000007 
B)  0.0000007 
C)  0.00000001 
D)  0.000007 
A)  0.00000007 
B)  0.0000007 
C)  0.00000001 
D)  0.000007

Question 15

Determine whether the sequence is arithmetic.
-$5 , - 15,45 , - 135,405 , \ldots$

Accepted Answer

A)  Arithmetic 
B)  Not arithmetic 
A)  Arithmetic 
B)  Not arithmetic

Question 16

Expand the expression using the Binomial Theorem.
-$$( 2 x + y ) ^ { 6 }$$

Accepted Answer

A)  $64 x ^ { 6 } + 192 x ^ { 5 } y + 480 x ^ { 4 } y ^ { 2 } + 960 x ^ { 3 } y ^ { 3 } + 1440 x ^ { 2 } y ^ { 4 } + 12 x y ^ { 5 } + y ^ { 6 }$ 
B)  $64 x ^ { 6 } + 192 x ^ { 5 } y + 240 x ^ { 4 } y ^ { 2 } + 160 x ^ { 3 } y ^ { 3 } + 60 x ^ { 2 } y ^ { 4 } + 12 x y ^ { 5 } + y ^ { 6 }$ 
C)  $64 x ^ { 6 } + 192 x ^ { 5 } y + 240 x ^ { 4 } y ^ { 2 } + 160 x ^ { 3 } y ^ { 3 } + 240 x ^ { 2 } y ^ { 4 } + 192 x y ^ { 5 } + 64 y ^ { 6 }$ 
D)  $2 x ^ { 6 } + 12 x ^ { 5 } y + 30 x ^ { 4 } y ^ { 2 } + 40 x ^ { 3 } y ^ { 3 } + 12 x y ^ { 5 } + y ^ { 6 }$ 
A)  $64 x ^ { 6 } + 192 x ^ { 5 } y + 480 x ^ { 4 } y ^ { 2 } + 960 x ^ { 3 } y ^ { 3 } + 1440 x ^ { 2 } y ^ { 4 } + 12 x y ^ { 5 } + y ^ { 6 }$ 
B)  $64 x ^ { 6 } + 192 x ^ { 5 } y + 240 x ^ { 4 } y ^ { 2 } + 160 x ^ { 3 } y ^ { 3 } + 60 x ^ { 2 } y ^ { 4 } + 12 x y ^ { 5 } + y ^ { 6 }$ 
C)  $64 x ^ { 6 } + 192 x ^ { 5 } y + 240 x ^ { 4 } y ^ { 2 } + 160 x ^ { 3 } y ^ { 3 } + 240 x ^ { 2 } y ^ { 4 } + 192 x y ^ { 5 } + 64 y ^ { 6 }$ 
D)  $2 x ^ { 6 } + 12 x ^ { 5 } y + 30 x ^ { 4 } y ^ { 2 } + 40 x ^ { 3 } y ^ { 3 } + 12 x y ^ { 5 } + y ^ { 6 }$

Question 17

Find the sum.
-$$\frac { 1 } { 7 } + \frac { 3 } { 7 } + \frac { 3 ^ { 2 } } { 7 } + \frac { 3 ^ { 3 } } { 7 } + \cdots + \frac { 3 ^ { n - 1 } } { 7 }$$

Accepted Answer

A)  $- \frac { 1 } { 7 } \left( 1 - 3 ^ { n } \right)$ 
B)  $\frac { 1 } { 14 } \left( 1 - 3 ^ { n } \right)$ 
C)  $- \frac { 2 } { 7 } \left( 1 - 3 ^ { n } \right)$ 
D)  $- \frac { 1 } { 14 } \left( 1 - 3 ^ { n } \right)$ 
A)  $- \frac { 1 } { 7 } \left( 1 - 3 ^ { n } \right)$ 
B)  $\frac { 1 } { 14 } \left( 1 - 3 ^ { n } \right)$ 
C)  $- \frac { 2 } { 7 } \left( 1 - 3 ^ { n } \right)$ 
D)  $- \frac { 1 } { 14 } \left( 1 - 3 ^ { n } \right)$

Question 18

Write out the sum. Do not evaluate.
-$$\sum _ { k = 1 } ^ { 4 } ( k + 6 )$$

Accepted Answer

A)  $10 + 11 + 12 + 13$ 
B)  $7 + 8 + 9 + 10$ 
C)  $7 + 8 + 9 + 10 + \ldots$ 
D)  $6 + 7 + 8 + 9$ 
A)  $10 + 11 + 12 + 13$ 
B)  $7 + 8 + 9 + 10$ 
C)  $7 + 8 + 9 + 10 + \ldots$ 
D)  $6 + 7 + 8 + 9$

Question 19

Solve the problem.
-For the geometric sequence $2,1 , \frac { 1 } { 2 } , \frac { 1 } { 4 } , \ldots$, find $\mathrm { a } _ { \mathrm { n } }$.

Accepted Answer

A)  $a _ { n } = 2 ^ { 1 - n }$ 
B)  $a _ { n } = \left( \frac { 1 } { 2 } \right) ^ { 1 - n }$ 
C)  $a _ { n } = 2 ^ { n - 2 }$ 
D)  $a _ { n } = \left( \frac { 1 } { 2 } \right) ^ { n - 2 }$ 
A)  $a _ { n } = 2 ^ { 1 - n }$ 
B)  $a _ { n } = \left( \frac { 1 } { 2 } \right) ^ { 1 - n }$ 
C)  $a _ { n } = 2 ^ { n - 2 }$ 
D)  $a _ { n } = \left( \frac { 1 } { 2 } \right) ^ { n - 2 }$

Question 20

Write the word or phrase that best completes each statement or answers the question.
-$$a _ { 1 } = 135 \text { and } a _ { n + 1 } = \frac { 1 } { 3 } \left( a _ { n } \right) \text { for } n \geq 2$$

Accepted Answer

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

Solve the problem. - $\text { Find the } 10 \text { th term of the geometric sequence } \frac { 1 } { 3 } , 1,3 , \ldots$

Find the indicated term using the given information. - $5,2 , - 1 , \ldots ;$ a 44

Find the indicated term using the given information. - $\mathrm { a } _ { 45 } = - \frac { 147 } { 5 } , \mathrm { a } _ { 13 } = - \frac { 51 } { 5 } ; \mathrm { a } _ { 3 }$

Write the word or phrase that best completes each statement or answers the question. -For the geometric sequence 64, 16, 4, 1, ... , find an.

If the sequence is geometric, find the common ratio. If the sequence is not geometric, say so. - $\frac { 3 } { 4 } , \frac { 3 } { 16 } , \frac { 3 } { 64 } , \frac { 3 } { 256 } , \frac { 3 } { 1,024 }$

Use the formula for the general term (the nth term) of a geometric sequence to find the indicated term of the sequence with the given first term, a1, and common ratio, r. -Find a9 when a1 = 2, r = -2.

Choose the one alternative that best completes the statement or answers the question. Evaluate the expression. - $\left( \begin{array} { l } 6 \\ 0 \end{array} \right)$

Use the formula for the general term (the nth term) of a geometric sequence to find the indicated term of the sequence with the given first term, a1, and common ratio, r. -Find ag when $a _ { 1 } = 50,000 , r = 0.1$ .

Solve the problem. -Suppose that certain bacteria can double their size and divide every 30 minutes. Write a recursive sequence that describes this growth where each value of $\mathrm { n }$ represents a 30 -minute interval. Let a $1 = 490$ represent the initial number of bacteria present.

Solve the problem. -The population of a town is increasing by 300 inhabitants each year. If its population at the beginning of 1990 was 26,587, what was its population at the beginning of 1996?

Determine whether the infinite geometric series converges or diverges. If it converges, find its sum. - $20 + 10 + 5 + \cdots$

Express the sum using summation notation. - $\frac { 5 ^ { 14 } } { 9 ^ { 4 } } + \frac { 5 ^ { 13 } } { 9 ^ { 5 } } + \frac { 5 ^ { 12 } } { 9 ^ { 6 } } + \ldots + \frac { 5 ^ { 7 } } { 9 ^ { 11 } }$

Use a graphing utility to find the sum of the geometric sequence. Round answer to two decimal places, if necessary. - $\sum _ { k = 1 } ^ { 12 } \frac { 1 } { 7 } \cdot ( - 2 ) ^ { \mathrm { k } - 1 }$

Use the formula for the general term (the nth term) of a geometric sequence to find the indicated term of the sequence with the given first term, a1, and common ratio, r. -Find a7 for the sequence 0.7, 0.07, 0.007, . . .

Determine whether the sequence is arithmetic. - $5 , - 15,45 , - 135,405 , \ldots$

Expand the expression using the Binomial Theorem. - $( 2 x + y ) ^ { 6 }$

Find the sum. - $\frac { 1 } { 7 } + \frac { 3 } { 7 } + \frac { 3 ^ { 2 } } { 7 } + \frac { 3 ^ { 3 } } { 7 } + \cdots + \frac { 3 ^ { n - 1 } } { 7 }$

Write out the sum. Do not evaluate. - $\sum _ { k = 1 } ^ { 4 } ( k + 6 )$

Solve the problem. -For the geometric sequence $2,1 , \frac { 1 } { 2 } , \frac { 1 } { 4 } , \ldots$ , find $\mathrm { a } _ { \mathrm { n } }$ .

Write the word or phrase that best completes each statement or answers the question. - $a _ { 1 } = 135 \text { and } a _ { n + 1 } = \frac { 1 } { 3 } \left( a _ { n } \right) \text { for } n \geq 2$

Functions and Their Graphs

Linear and Quadratic Functions

Polynomial and Rational Functions

Exponential and Logarithmic Functions

Trigonometric Functions

Analytic Trigonometry

Applications of Trigonometric Functions

Polar Coordinates; Vectors

Analytic Geometry

Systems of Equations and Inequalities

Counting and Probability

A Preview of Calculus: the Limit, Derivative, and Integral of a Function

Foundations: a Prelude to Functions

Graphing Utilities

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Exam 11: Sequences; Induction; the Binomial Theorem

Solve the problem. - Find the 10 th term of the geometric sequence 13,1,3,…\text { Find the } 10 \text { th term of the geometric sequence } \frac { 1 } { 3 } , 1,3 , \ldots Find the 10 th term of the geometric sequence 31​,1,3,…

Find the indicated term using the given information. - 5,2,−1,…;5,2 , - 1 , \ldots ;5,2,−1,…; a 44

Find the indicated term using the given information. - a45=−1475,a13=−515;a3\mathrm { a } _ { 45 } = - \frac { 147 } { 5 } , \mathrm { a } _ { 13 } = - \frac { 51 } { 5 } ; \mathrm { a } _ { 3 }a45​=−5147​,a13​=−551​;a3​