Question 1

Write out the first five terms of the sequence.
-$\left\{ 2 ^ { n } \right\}$

Accepted Answer

A)  $2,4,8,16,32$ 
B)  $1,2,4,8,16$ 
C)  $4,8,16,32,64$ 
D)  $1,4,9,16,25$ 
A)  $2,4,8,16,32$ 
B)  $1,2,4,8,16$ 
C)  $4,8,16,32,64$ 
D)  $1,4,9,16,25$

Question 2

Find the nth term and the indicated term of the arithmetic sequence whose initial term, a, and common difference, d, are
given.
-$$\begin{array} { l } 
a = 9 ; d = 4 \
a _ { n } = ? ; a _ { 14 } = \text { ? }
\end{array}$$

Accepted Answer

A)  $a _ { n } = 5 - 4 n ; a _ { 14 } = 61$ 
B)  $a _ { n } = 5 + 4 n ; a _ { 14 } = 61$ 
C)  $a _ { n } = 9 + 4 n ; a _ { 14 } = 61$ 
D)  $a _ { n } = 5 + 4 n ; a _ { 14 } = 29$ 
A)  $a _ { n } = 5 - 4 n ; a _ { 14 } = 61$ 
B)  $a _ { n } = 5 + 4 n ; a _ { 14 } = 61$ 
C)  $a _ { n } = 9 + 4 n ; a _ { 14 } = 61$ 
D)  $a _ { n } = 5 + 4 n ; a _ { 14 } = 29$

Question 3

Determine whether the sequence is geometric.
-3, 1, -1, -3, -5, ...

Accepted Answer

A)  Geometric 
B)  Not geometric 
A)  Geometric 
B)  Not geometric

Question 4

Find the indicated term of the sequence.
-The thirteenth term of the arithmetic sequence $0,9,18 , \ldots$

Accepted Answer

A)  117 
B)  96 
C)  108 
D)  126 
A)  117 
B)  96 
C)  108 
D)  126

Question 5

Choose the one alternative that best completes the statement or answers the question.
Evaluate the expression.
-$\left( \begin{array} { l } 9 \ 9 \end{array} \right)$

Accepted Answer

A)  1 
B)  362,880 
C)  0 
D)  2 
A)  1 
B)  362,880 
C)  0 
D)  2

Question 6

Write the word or phrase that best completes each statement or answers the question.
Use the Principle of Mathematical Induction to show that the statement is true for all natural numbers n.
-$$1 \cdot 1 + 2 \cdot 1 + 3 \cdot 1 + \ldots + n = \frac { n ( n + 1 ) } { 2 }$$

Accepted Answer

First we show that the statement is true

Question 7

Find the sum.
-$$\sum _ { k = 1 } ^ { 3 } \left( \frac { 2 } { 3 } \right) ^ { k + 1 }$$

Accepted Answer

A)  $\frac { 38 } { 27 }$ 
B)  $\frac { 76 } { 81 }$ 
C)  $\frac { 260 } { 81 }$ 
D)  $\frac { 80 } { 81 }$ 
A)  $\frac { 38 } { 27 }$ 
B)  $\frac { 76 } { 81 }$ 
C)  $\frac { 260 } { 81 }$ 
D)  $\frac { 80 } { 81 }$

Question 8

Write the word or phrase that best completes each statement or answers the question.
-$$( g - 2 h ) ^ { 3 }$$

Accepted Answer

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

Question 9

Find the fifth term and the nth term of the geometric sequence whose initial term, a, and common ratio, r, are given.
-$$a = 7 ; r = - 2$$

Accepted Answer

A)  $\mathrm { a } _ { 5 } = - 56 ; \mathrm { a } _ { \mathrm { n } } = 7 \cdot ( - 2 ) ^ { \mathrm { n } }$ 
B)  $\mathrm { a } _ { 5 } = 112 ; \mathrm { a } _ { \mathrm { n } } = 7 \cdot ( - 2 ) ^ { \mathrm { n } }$ 
C)  $a _ { 5 } = 112 ; a _ { n } = 7 \cdot ( - 2 ) ^ { n - 1 }$ 
D)  $a _ { 5 } = - 56 ; a _ { n } = 7 \cdot ( - 2 ) ^ { n - 1 }$ 
A)  $\mathrm { a } _ { 5 } = - 56 ; \mathrm { a } _ { \mathrm { n } } = 7 \cdot ( - 2 ) ^ { \mathrm { n } }$ 
B)  $\mathrm { a } _ { 5 } = 112 ; \mathrm { a } _ { \mathrm { n } } = 7 \cdot ( - 2 ) ^ { \mathrm { n } }$ 
C)  $a _ { 5 } = 112 ; a _ { n } = 7 \cdot ( - 2 ) ^ { n - 1 }$ 
D)  $a _ { 5 } = - 56 ; a _ { n } = 7 \cdot ( - 2 ) ^ { n - 1 }$

Question 10

Determine whether the sequence is geometric.
-3, 6, 12, 24, 48, ...

Accepted Answer

A)  Geometric 
B)  Not geometric 
A)  Geometric 
B)  Not geometric

Question 11

Write the word or phrase that best completes each statement or answers the question.
-A ball is dropped from a height of 25 feet. Each time it strikes the ground, it bounces up to 0.7 of the previous
height. The total distance the ball has travelled before the second bounce is 25 + 2(25 · 0.7) feet, and the total
distance the ball has travelled before bounce n + 1 is $$25 + \sum _ { k = 1 } ^ { n } 50 \left( 0.7 ^ { k } \right) \text { feet. }$$ Use facts about infinite geometric series to calculate the total distance the ball has travelled by the time it has stopped
bouncing.

Accepted Answer

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

Question 12

Find the sum.
-2, -4, 8, -16, 32

Accepted Answer

A)  -62 
B)  62 
C)  -22 
D)  22 
A)  -62 
B)  62 
C)  -22 
D)  22

Question 13

Find the indicated coefficient or term.
-The coefficient of $x$ in the expansion of $( 3 x + 4 ) ^ { 5 }$

Accepted Answer

A)  960 
B)  3,840 
C)  5,120 
D)  2,880 
A)  960 
B)  3,840 
C)  5,120 
D)  2,880

Question 14

Find the sum.
-$$\sum _ { \mathrm { k } = 1 } ^ { 5 } \left( \frac { 1 } { 3 } \right) ( 4 ) ^ { \mathrm { k } }$$

Accepted Answer

A)  $\frac { 1,373 } { 3 }$ 
B)  $\frac { 1,385 } { 3 }$ 
C)  $\frac { 1,364 } { 3 }$ 
D)  $\frac { 1,376 } { 3 }$ 
A)  $\frac { 1,373 } { 3 }$ 
B)  $\frac { 1,385 } { 3 }$ 
C)  $\frac { 1,364 } { 3 }$ 
D)  $\frac { 1,376 } { 3 }$

Question 15

Find the nth term of the geometric sequence.
-$5 , - 15,45 , - 135,405$

Accepted Answer

A)  $a _ { n } = 5 \cdot ( - 3 ) ^ { n - 1 }$ 
B)  $a _ { n } = 5 \cdot ( - 3 ) n$ 
C)  $a _ { n } = a _ { 1 } - 3 ^ { n }$ 
D)  $a _ { n } = 5 \cdot ( - 3 ) ^ { n }$ 
A)  $a _ { n } = 5 \cdot ( - 3 ) ^ { n - 1 }$ 
B)  $a _ { n } = 5 \cdot ( - 3 ) n$ 
C)  $a _ { n } = a _ { 1 } - 3 ^ { n }$ 
D)  $a _ { n } = 5 \cdot ( - 3 ) ^ { n }$

Question 16

Choose the one alternative that best completes the statement or answers the question.
-The 12 th term in the expansion of $( x - 2 y ) ^ { 13 }$

Accepted Answer

A)  $79,872 x ^ { 11 } \mathrm { y } ^ { 2 }$ 
B)  $79,872 x ^ { 2 } y ^{12}$ 
C)  $- 159,744 \times 11 \mathrm { y } ^ { 2 }$ 
D)  $- 159,744 x ^ { 2 } y ^ { 11 }$ 
A)  $79,872 x ^ { 11 } \mathrm { y } ^ { 2 }$ 
B)  $79,872 x ^ { 2 } y ^{12}$ 
C)  $- 159,744 \times 11 \mathrm { y } ^ { 2 }$ 
D)  $- 159,744 x ^ { 2 } y ^ { 11 }$

Question 17

Write out the sum. Do not evaluate.
-$$\sum _ { k = 1 } ^ { 4 } \left( k ^ { 2 } - 4 k - 3 \right)$$

Accepted Answer

A)  $1 - 6 - 7 - 6$ 
B)  $- 6 - 7 - 6 - 3$ 
C)  $- 6 - 7 - 6 - 3 + \ldots$ 
D)  $- 6 + 7 - 6 + 3$ 
A)  $1 - 6 - 7 - 6$ 
B)  $- 6 - 7 - 6 - 3$ 
C)  $- 6 - 7 - 6 - 3 + \ldots$ 
D)  $- 6 + 7 - 6 + 3$

Question 18

Write the word or phrase that best completes each statement or answers the question.
Use the Principle of Mathematical Induction to show that the statement is true for all natural numbers n.
-Use the Principle of Mathematical Induction to show that the statement "5 is a factor of $7 ^ { \mathrm { n } } - 2 ^ { \mathrm { n } }$ " is true for all natural numbers. (Hint: $7 ^ { \mathrm { k } + 1 } - 2 ^ { \mathrm { k } + 1 } = 7 \left( 7 ^ { \mathrm { k } } - 2 ^ { \mathrm { k } } \right) + 5 \cdot 2 ^ { \mathrm { k } }$ )

Accepted Answer

When @#LAT-DLM&, so the statement is true when @#LAT-DLM&. A

Question 19

If the sequence is geometric, find the common ratio. If the sequence is not geometric, say so.
-$$4 , - 12,36 , - 108,324$$

Accepted Answer

A)  $- 3$ 
B)  $- 16$ 
C)  3 
D)  Not geometric 
A)  $- 3$ 
B)  $- 16$ 
C)  3 
D)  Not geometric

Question 20

Evaluate the factorial expression.
-$\frac { 8 ! } { 7 ! }$

Accepted Answer

A)  $\frac { 8 } { 7 }$ 
B)  8 
C)  1 
D)  8 ! 
A)  $\frac { 8 } { 7 }$ 
B)  8 
C)  1 
D)  8 !

Write out the first five terms of the sequence. - $\left\{ 2 ^ { n } \right\}$

Find the nth term and the indicated term of the arithmetic sequence whose initial term, a, and common difference, d, are given. - a=9;d=4 =?;= ?

Determine whether the sequence is geometric. -3, 1, -1, -3, -5, ...

Find the indicated term of the sequence. -The thirteenth term of the arithmetic sequence $0,9,18 , \ldots$

Choose the one alternative that best completes the statement or answers the question. Evaluate the expression. - $\left( \begin{array} { l } 9 \\ 9 \end{array} \right)$

Write the word or phrase that best completes each statement or answers the question. Use the Principle of Mathematical Induction to show that the statement is true for all natural numbers n. - $1 \cdot 1 + 2 \cdot 1 + 3 \cdot 1 + \ldots + n = \frac { n ( n + 1 ) } { 2 }$

Find the sum. - $\sum _ { k = 1 } ^ { 3 } \left( \frac { 2 } { 3 } \right) ^ { k + 1 }$

Write the word or phrase that best completes each statement or answers the question. - $( g - 2 h ) ^ { 3 }$

Find the fifth term and the nth term of the geometric sequence whose initial term, a, and common ratio, r, are given. - $a = 7 ; r = - 2$

Determine whether the sequence is geometric. -3, 6, 12, 24, 48, ...

Find the sum. -2, -4, 8, -16, 32

Find the indicated coefficient or term. -The coefficient of $x$ in the expansion of $( 3 x + 4 ) ^ { 5 }$

Find the sum. - $\sum _ { \mathrm { k } = 1 } ^ { 5 } \left( \frac { 1 } { 3 } \right) ( 4 ) ^ { \mathrm { k } }$

Find the nth term of the geometric sequence. - $5 , - 15,45 , - 135,405$

Choose the one alternative that best completes the statement or answers the question. -The 12 th term in the expansion of $( x - 2 y ) ^ { 13 }$

Write out the sum. Do not evaluate. - $\sum _ { k = 1 } ^ { 4 } \left( k ^ { 2 } - 4 k - 3 \right)$

If the sequence is geometric, find the common ratio. If the sequence is not geometric, say so. - $4 , - 12,36 , - 108,324$

Evaluate the factorial expression. - $\frac { 8 ! } { 7 ! }$

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Exam 11: Sequences; Induction; the Binomial Theorem

Write out the first five terms of the sequence. - {2n}\left\{ 2 ^ { n } \right\}{2n}