Question 1

Find the indicated term using the given information.
-a = 4 , d = 4 ; a8

Accepted Answer

A)  32 
B)  36 
C)  -28 
D)  -24 
A)  32 
B)  36 
C)  -28 
D)  -24

Question 2

Choose the one alternative that best completes the statement or answers the question.
-The 5 th term in the expansion of $( 2 x + 5 ) ^ { 5 }$

Accepted Answer

A)  15,625 
B)  $2,500 x ^ { 2 }$ 
C)  $1,250 \mathrm { x }$ 
D)  $6,250 \mathrm { x }$ 
A)  15,625 
B)  $2,500 x ^ { 2 }$ 
C)  $1,250 \mathrm { x }$ 
D)  $6,250 \mathrm { x }$

Question 3

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

Accepted Answer

A)  $- 2 , - 1,0,1,2$ 
B)  $- 1,0,1,2,3$ 
C)  $- 3 , - 2 , - 1,0,1$ 
D)  $2,4,6,8,10$ 
A)  $- 2 , - 1,0,1,2$ 
B)  $- 1,0,1,2,3$ 
C)  $- 3 , - 2 , - 1,0,1$ 
D)  $2,4,6,8,10$

Question 4

Choose the one alternative that best completes the statement or answers the question.
-Jennifer takes a job with a starting salary of $40,000 for the first year with an annual increase of 4% beginning in the second year. What is Jennifer's salary, to the nearest dollar, in the sixth year?

Accepted Answer

A)  $48,666 
B)  $50,891 
C)  $49,664 
D)  $47,367 
A)  $48,666 
B)  $50,891 
C)  $49,664 
D)  $47,367

Question 5

Determine whether the infinite geometric series converges or diverges. If it converges, find its sum.
-$$1 + \frac { 1 } { 2 } + \frac { 1 } { 4 } + \cdots$$

Accepted Answer

A)  Converges; 2 
B)  Converges; 1 
C)  Converges; $\frac { 3 } { 2 }$ 
D)  Converges; $\frac { 1 } { 2 }$ 
A)  Converges; 2 
B)  Converges; 1 
C)  Converges; $\frac { 3 } { 2 }$ 
D)  Converges; $\frac { 1 } { 2 }$

Question 6

Determine whether the sequence is geometric.
-3, 5, 7, 11, 13, ...

Accepted Answer

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

Question 7

Choose the one alternative that best completes the statement or answers the question.
-A particular substance decays in such a way that it loses half its weight each day. How much of the substance is left after 7 days if it starts out at 16 grams?

Accepted Answer

A)  4 grams 
B)  $\frac { 1 } { 8 }$ gram 
C)  $\frac { 1 } { 4 }$ gram 
D)  8 grams 
A)  4 grams 
B)  $\frac { 1 } { 8 }$ gram 
C)  $\frac { 1 } { 4 }$ gram 
D)  8 grams

Question 8

Express the repeating decimal as a fraction in lowest terms.
-$0 . \overline { 77 } = \frac { 77 } { 100 } + \frac { 77 } { 10,000 } + \frac { 77 } { 1,000,000 } + \ldots$

Accepted Answer

A)  $\frac { 7777 } { 10000 }$ 
B)  $\frac { 7777 } { 999 }$ 
C)  $\frac { 7 } { 9 }$ 
D)  $\frac { 7700 } { 999 }$ 
A)  $\frac { 7777 } { 10000 }$ 
B)  $\frac { 7777 } { 999 }$ 
C)  $\frac { 7 } { 9 }$ 
D)  $\frac { 7700 } { 999 }$

Question 9

Determine whether the sequence is geometric.
-4, -12, 36, -108, 324, ...

Accepted Answer

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

Question 10

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.
-$$3 + 3 \cdot \frac { 1 } { 7 } + 3 \cdot \left( \frac { 1 } { 7 } \right) ^ { 2 } + \ldots + 3 \cdot \left( \frac { 1 } { 7 } \right) ^ { n - 1 } = \frac { 3 \left( 1 - \left( \frac { 1 } { 7 } \right) ^ { n } \right) } { 1 - \frac { 1 } { 7 } }$$

Accepted Answer

\[\begin{array} { l } 
= \frac { 3 \left

Question 11

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.
-$$n ^ { 2 } - n + 2 \text { is divisible by } 2$$

Accepted Answer

First, we show that the statement is tru

Question 12

Expand the expression using the Binomial Theorem.
-$$\left( 4 x ^ { 2 } - 1 \right) ^ { 3 }$$

Accepted Answer

A)  $64 x ^ { 3 } - 48 x ^ { 2 } + 12 x - 1$ 
B)  $64 x ^ { 6 } - 48 x ^ { 4 } + 12 x ^ { 2 } - 1$ 
C)  $256 x ^ { 8 } + 64 x ^ { 6 } - 48 x ^ { 4 } + 12 x ^ { 2 } - 1$ 
D)  $\left( 16 x ^ { 4 } - 8 x ^ { 2 } + 1 \right) ^ { 3 }$ 
A)  $64 x ^ { 3 } - 48 x ^ { 2 } + 12 x - 1$ 
B)  $64 x ^ { 6 } - 48 x ^ { 4 } + 12 x ^ { 2 } - 1$ 
C)  $256 x ^ { 8 } + 64 x ^ { 6 } - 48 x ^ { 4 } + 12 x ^ { 2 } - 1$ 
D)  $\left( 16 x ^ { 4 } - 8 x ^ { 2 } + 1 \right) ^ { 3 }$

Question 13

Evaluate the factorial expression.
-$\frac { 5 ! } { 3 ! }$

Accepted Answer

A)  2 ! 
B)  5 
C)  $\frac { 5 } { 3 }$ 
D)  20 
A)  2 ! 
B)  5 
C)  $\frac { 5 } { 3 }$ 
D)  20

Question 14

Find the fifth term and the nth term of the geometric sequence whose initial term, a, and common ratio, r, are given.
-a = -8; r = -5

Accepted Answer

A)  a5 = 1,000; an = -8 ·(-5)n 
B)  a5 = -5,000; an = -8 ·(-5)n 
C)  a5 = -5,000; an = -8 ·(-5)n-1 
D)  a5 = 1,000; an = -8 ·(-5)n-1 
A)  a5 = 1,000; an = -8 ·(-5)n 
B)  a5 = -5,000; an = -8 ·(-5)n 
C)  a5 = -5,000; an = -8 ·(-5)n-1 
D)  a5 = 1,000; an = -8 ·(-5)n-1

Question 15

Choose the one alternative that best completes the statement or answers the question.
Evaluate the expression.
-$\left( \begin{array} { l } 4 \ 1 \end{array} \right)$

Accepted Answer

A)  $\frac { 4 } { 2 }$ 
B)  4 
C)  1 
D)  $4 !$ 
A)  $\frac { 4 } { 2 }$ 
B)  4 
C)  1 
D)  $4 !$

Question 16

Find the sum of the sequence.
-$$\sum _ { k = 2 } ^ { 4 } k ( k + 5 )$$

Accepted Answer

A)  74 
B)  80 
C)  33 
D)  50 
A)  74 
B)  80 
C)  33 
D)  50

Question 17

Choose the one alternative that best completes the statement or answers the question.
-A pendulum bob swings through an arc 40 inches long on its first swing. Each swing thereafter, it swings only 63% as far as on the previous swing. What is the length of the arc after 9 swings? Round your answer to two
Decimal places, if necessary.

Accepted Answer

A)  0.63 inches 
B)  201.6 inches 
C)  0.39 inches 
D)  0.99 inches 
A)  0.63 inches 
B)  201.6 inches 
C)  0.39 inches 
D)  0.99 inches

Question 18

Express the sum using summation notation with a lower limit of summation not necessarily 1 and with k for the index of
summation.
-$$\frac { 4 } { 5 } + \frac { 5 } { 6 } + \frac { 6 } { 7 } + \frac { 7 } { 8 } + \ldots + \frac { 17 } { 18 }$$

Accepted Answer

A)  $\sum _ { k = 5 } ^ { 17 } \frac { \mathrm { k } } { \mathrm { k } + 1 }$ 
B)  $\sum _ { k = 4 } ^ { 17 } \frac { \mathrm { k } + 1 } { \mathrm { k } }$ 
C)  $\sum _ { k = 4 } ^ { 17 } \frac { k } { k + 1 }$ 
D)  $\sum _ { \mathrm { k } = 4 } ^ { 17 } \frac { \mathrm { k } } { \mathrm { k } \cdot 1.5 }$ 
A)  $\sum _ { k = 5 } ^ { 17 } \frac { \mathrm { k } } { \mathrm { k } + 1 }$ 
B)  $\sum _ { k = 4 } ^ { 17 } \frac { \mathrm { k } + 1 } { \mathrm { k } }$ 
C)  $\sum _ { k = 4 } ^ { 17 } \frac { k } { k + 1 }$ 
D)  $\sum _ { \mathrm { k } = 4 } ^ { 17 } \frac { \mathrm { k } } { \mathrm { k } \cdot 1.5 }$

Question 19

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.
-$$1 ^ { 2 } + 4 ^ { 2 } + 7 ^ { 2 } + \ldots + ( 3 n - 2 ) ^ { 2 } = \frac { n \left( 6 n ^ { 2 } - 3 n - 1 \right) } { 2 }$$

Accepted Answer

@#LAT-DLM&
Condition II is sat

Question 20

If the sequence is geometric, find the common ratio. If the sequence is not geometric, say so.
-24, 9.6, 3.84, 1.536, $0.61$

Accepted Answer

A)  $2.5$ 
B)  $- 0.4$ 
C)  $0.4$ 
D)  $0.61$ 
A)  $2.5$ 
B)  $- 0.4$ 
C)  $0.4$ 
D)  $0.61$

Find the indicated term using the given information. -a = 4 , d = 4 ; a8

Choose the one alternative that best completes the statement or answers the question. -The 5 th term in the expansion of $( 2 x + 5 ) ^ { 5 }$

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

Choose the one alternative that best completes the statement or answers the question. -Jennifer takes a job with a starting salary of $40,000 for the first year with an annual increase of 4% beginning in the second year. What is Jennifer's salary, to the nearest dollar, in the sixth year?

Determine whether the infinite geometric series converges or diverges. If it converges, find its sum. - $1 + \frac { 1 } { 2 } + \frac { 1 } { 4 } + \cdots$

Determine whether the sequence is geometric. -3, 5, 7, 11, 13, ...

Choose the one alternative that best completes the statement or answers the question. -A particular substance decays in such a way that it loses half its weight each day. How much of the substance is left after 7 days if it starts out at 16 grams?

Express the repeating decimal as a fraction in lowest terms. - $0 . \overline { 77 } = \frac { 77 } { 100 } + \frac { 77 } { 10,000 } + \frac { 77 } { 1,000,000 } + \ldots$

Determine whether the sequence is geometric. -4, -12, 36, -108, 324, ...

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. - $n ^ { 2 } - n + 2 \text { is divisible by } 2$

Expand the expression using the Binomial Theorem. - $\left( 4 x ^ { 2 } - 1 \right) ^ { 3 }$

Evaluate the factorial expression. - $\frac { 5 ! } { 3 ! }$

Find the fifth term and the nth term of the geometric sequence whose initial term, a, and common ratio, r, are given. -a = -8; r = -5

Choose the one alternative that best completes the statement or answers the question. Evaluate the expression. - $\left( \begin{array} { l } 4 \\ 1 \end{array} \right)$

Find the sum of the sequence. - $\sum _ { k = 2 } ^ { 4 } k ( k + 5 )$

Express the sum using summation notation with a lower limit of summation not necessarily 1 and with k for the index of summation. - $\frac { 4 } { 5 } + \frac { 5 } { 6 } + \frac { 6 } { 7 } + \frac { 7 } { 8 } + \ldots + \frac { 17 } { 18 }$

If the sequence is geometric, find the common ratio. If the sequence is not geometric, say so. -24, 9.6, 3.84, 1.536, $0.61$

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Exam 11: Sequences; Induction; the Binomial Theorem