Deck 11: Sequences; Induction; the Binomial Theorem

Question 1

Evaluate the factorial expression.

- $\frac { 8 ! } { 7 ! }$

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

Answer 1

8

Question 2

Evaluate the factorial expression.

- $\frac { 7 ! } { 5 ! 2 ! }$

A) 1
B) 21
C) 7
D) 0 !

Answer 2

21

Question 3

Evaluate the factorial expression.

- $$\frac { 6 ! } { 3 ! 3 ! }$$

A) 10
B) 40
C) 20
D) 120

Answer 3

20

Question 4

Write out the first five terms of the sequence.
{4(4n - 2)}

A) -8, 8, 24, 40, 56
B) 2, 6, 10, 14, 18
C) 8, 16, 24, 32, 40
D) 8, 24, 40, 56, 72

Question 5

Write out the first five terms of the sequence.

- $$\left\{ 2 ^ { n } \right\}$$

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 6

Evaluate the factorial expression.

- $\frac { 2 ! } { 4 ! }$

A) 12
B) $\frac { 1 } { 2 ! }$
C) $\frac { 1 } { 12 }$
D) 2 !

Question 7

Write the first four terms of the sequence whose general term is given.

- $$\left\{ \frac { - 2 ( n + 1 ) ! } { n ! } \right\}$$

A) $- 1,0,1,2$
B) $- 4 , - 3 , - \frac { 4 } { 3 } , - \frac { 5 } { 12 }$
C) $- 4 , - 3 , - \frac { 8 } { 3 } , - \frac { 5 } { 2 }$
D) $- 4 , - 6 , - 8 , - 10$

Question 8

Evaluate the factorial expression.

- $$\frac { ( \mathrm { n } + 9 ) ! } { \mathrm { n } + 9 }$$

A) $n + 9$ !
B) 1
C) $( n + 8 ) !$
D) 9 !

Question 9

Write out the first five terms of the sequence.

- $$\left\{ \frac { 4 } { n ^ { 2 } } \right\}$$

A) $4,1 , \frac { 4 } { 9 } , \frac { 1 } { 4 } , \frac { 4 } { 25 }$

B) $\frac { 1 } { 4 } , \frac { 2 } { 9 } , \frac { 3 } { 16 } , \frac { 4 } { 25 } , \frac { 5 } { 36 }$

C) $1 , \frac { 1 } { 2 } , \frac { 1 } { 3 } , \frac { 1 } { 4 } , \frac { 1 } { 5 }$

D) $1 , \frac { 1 } { 4 } , \frac { 1 } { 9 } , \frac { 1 } { 16 } , \frac { 1 } { 25 }$

Question 10

Write out the first five terms of the sequence.

- $$\left\{ n ^ { 2 } - n \right\}$$

A) 1, 4, 9, 16, 25
B) 0, 2, 6, 12, 20
C) 0, 3, 8, 15, 24
D) 2, 6, 12, 20, 30

Question 11

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

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 12

The given pattern continues. Write down the nth term of the sequence suggested by the pattern.

-8 , 20 , 32 , 44 , 56 , ...

A) $a _ { n } = 8 ( 12 ) ^ { n - 1 }$
B) $a _ { n } = 4 n - 12$
C) $a _ { n } = 12 n - 1$
D) $a _ { n } = 4 ( 3 n - 1 )$

Question 13

The given pattern continues. Write down the nth term of the sequence suggested by the pattern.

-1 , 4 , 7 , 10 , 13 , ...

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

Question 14

Evaluate the factorial expression.

- $\frac { 5 ! } { 3 ! }$

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

Question 15

Write out the first five terms of the sequence.
{4n - 2}

A) 6, 10, 14, 18, 22
B) 2, 3, 4, 5, 6
C) -2, -6, -10, -14, -18
D) 2, 6, 10, 14, 18

Question 16

Write the first four terms of the sequence whose general term is given.

- $\left\{ \frac { 3 ^ { n } } { ( n + 3 ) ! } \right\}$

A) $\frac { 1 } { 8 } , \frac { 3 } { 40 } , \frac { 3 } { 80 } , \frac { 9 } { 560 }$

B) $\frac { 1 } { 8 } , \frac { 3 } { 40 } , \frac { 3 } { 40 } , \frac { 9 } { 280 }$

C) $\frac { 3 } { 7 } , \frac { 9 } { 8 } , 3 , \frac { 81 } { 10 }$

D) $\frac { 3 } { 4 } , \frac { 9 } { 5 } , \frac { 9 } { 2 } , \frac { 81 } { 7 }$

Question 17

Write out the first five terms of the sequence.

- $$\left\{ ( - 1 ) ^ { n - 1 } \left( \frac { n + 1 } { 2 n - 1 } \right) \right\}$$

A) $- 2,1 , \frac { 4 } { 5 } , - \frac { 5 } { 7 } , \frac { 2 } { 3 }$

B) $2 , - 1 , \frac { 4 } { 5 } , - \frac { 5 } { 7 } , \frac { 2 } { 3 }$

C) $2,1 , \frac { 4 } { 5 } , \frac { 5 } { 7 } , \frac { 2 } { 3 }$

D) $- 2,1 , - \frac { 4 } { 5 } , \frac { 5 } { 7 } , - \frac { 2 } { 3 }$

Question 18

Write out the first five terms of the sequence.

- $$\left\{ \frac { ( 2 n - 1 ) ! } { n ! } \right\}$$

A) $2,6,40,1260,72,576$

B) $1,6,40,1260,72,576$

C) $2,3,20,210,3024$

D) $1,3,20,210,3024$

Question 19

Write out the first five terms of the sequence.

- $\left\{ \frac { n } { n ^ { 2 } + 2 } \right\}$

A) $\frac { 1 } { 4 } , \frac { 1 } { 3 } , \frac { 3 } { 8 } , \frac { 2 } { 5 } , \frac { 5 } { 12 }$

B) $\frac { 1 } { 3 } , \frac { 1 } { 3 } , \frac { 3 } { 11 } , \frac { 2 } { 9 } , \frac { 5 } { 27 }$

C) $\frac { 1 } { 3 } , \frac { 1 } { 3 } , \frac { 3 } { 8 } , \frac { 2 } { 5 } , \frac { 5 } { 12 }$

D) $\frac { 1 } { 2 } , \frac { 1 } { 3 } , \frac { 3 } { 8 } , \frac { 2 } { 5 } , \frac { 5 } { 12 }$

Question 20

Evaluate the factorial expression.

- $$\frac { n ( n + 9 ) ! } { ( n + 10 ) ! }$$

A) $\frac { n } { 10 }$
B) $\frac { n } { n + 10 }$
C) $\frac { \mathrm { n } } { ( \mathrm { n } + 10 ) ! }$
D) $\frac { 1 } { n + 10 }$

Question 21

The given pattern continues. Write down the nth term of the sequence suggested by the pattern.

- $$\frac { 1 } { 1 } , \frac { 1 } { 4 } , \frac { 1 } { 9 } , \frac { 1 } { 16 } , \frac { 1 } { 25 } , \ldots$$

A) $a _ { n } = \frac { 1 } { 3 n - 2 }$
B) $a _ { n } = \left( \frac { 1 } { 2 } \right) ^ { n - 1 }$
C) $a _ { n } = \frac { 1 } { n ^ { n - 1 } }$
D) $a _ { n } = \frac { 1 } { n ^ { 2 } }$

Question 22

The sequence is defined recursively. Write the first four terms.

Question 23

The given pattern continues. Write down the nth term of the sequence suggested by the pattern.

-0, 2, 6, 12, 20, ...

A) $a _ { n } = 4 n - 6$
B) $a _ { n } = 2 ^ { n - 1 } - 1$
C) $a _ { n } = n ^ { 2 } - n$
D) $a _ { n } = 2 n - 2$

Question 24

Solve.
During a five-year period, a company doubles its profits each year. If the profits at the end of the fifth year are $ 192,000, then what are the profits for each of the first four years?

A) $13,000, $26,000, $52,000, $102,000
B) $12,000, $24,000, $36,000, $48,000
C) $12,000, $24,000, $48,000, $96,000
D) $12,000, $24,000, $48,000, $120,000

Question 25

The sequence is defined recursively. Write the first four terms.

- $$a _ { 1 } = \sqrt { 6 } ; a _ { n } = \sqrt { 6 a _ { n - 1 } }$$

A) $\sqrt { 6 } , 6,6 \sqrt { 6 } , 36$

B) $\sqrt { 6 } , \sqrt { \sqrt { 6 } } , \sqrt { \sqrt { \sqrt { 6 } } } , \sqrt { \sqrt { \sqrt { \sqrt { 6 } } } }$

C) $\sqrt { 6 } , 6 \sqrt { 6 } , 36 \sqrt { 6 } , 216 \sqrt { 6 }$

D) $\sqrt { 6 } , \sqrt { 6 \sqrt { 6 } } , \sqrt { 6 \sqrt { 6 \sqrt { 6 } } } , \sqrt { 6 \sqrt { 6 \sqrt { 6 \sqrt { 6 } } } }$

Question 26

Express the sum using summation notation.

- $$2 ^ { 3 } + 3 ^ { 3 } + 4 ^ { 3 } + \cdots + 8 ^ { 3 }$$

A)
$\sum _ { k = 1 } ^ { 8 } k ^ { 3 }$

B)

$\sum _ { k = 3 } ^ { 8 } ( k - 1 ) ^ { 3 }$

C)
$\sum _ { k = 2 } ^ { 8 } k ^ { 3 }$

D)
$\sum _ { k = 2 } ^ { n } k ^ { 3 }$

Question 27

The sequence is defined recursively. Write the first four terms.

- $$a _ { 1 } = z ^ { \prime } a _ { n } = a _ { n - 1 } + U$$

A) $U , U + z , U + 2 z , U + 3 z$
B) $z , z + U , z + 2 U , z + 3 U$
C) $\mathrm { z } , \mathrm { U } , 2 \mathrm { U } , 3 \mathrm { U }$
D) $z , z - U , z - 2 U , z - 3 U$

Question 28

Write out the sum. Do not evaluate.

- $$\sum _ { k = 1 } ^ { 4 } \left( k ^ { 2 } - 4 k - 3 \right)$$

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

Question 29

Write out the sum. Do not evaluate.

- $$\sum _ { k = 1 } ^ { 4 } ( k + 6 )$$

A) 10 + 11 + 12 + 13
B) 7 + 8 + 9 + 10
C) 7 + 8 + 9 + 10 + ...
D) 6 + 7 + 8 + 9

Question 30

Solve.

-The number of students in a school in year n is estimated by the model $$a _ { n } = 5 n ^ { 2 } + 14 n + 81$$ . About how many students are in the school in each of the first three years?

A) 100, 129, 153
B) 100, 129, 168
C) 114, 143, 182
D) 105, 129, 168

Question 31

The sequence is defined recursively. Write the first four terms.

- $$a _ { 1 } = 3 \text { and } a _ { n } = 2 a _ { n - 1 } \text { for } n \geq 2$$

A) 3, 5, 4, 3
B) 3, 6, 12, 24
C) 3, 8, 14, 26
D) 4, 8, 16, 32

Question 32

The sequence is defined recursively. Write the first four terms.

- $$a _ { 1 } = 2 \text { and } a _ { n } = a _ { n - 1 } - 4 \text { for } n \geq 2$$

A) -4, -8, -12, -16
B) 2, 6 , 10 , 14
C) 2, 0 , -4 , -8
D) 2, -2, -6, -10

Question 33

The sequence is defined recursively. Write the first four terms.

- $$a _ { 1 } = 4 \text { and } a _ { n } = 4 a _ { n - 1 } - 4 \text { for } n \geq 2$$

A) 4, 20, 84, 340
B) 4, 16, 64, 256
C) 4, 12, 60, 252
D) 4, 12, 44, 172

Question 34

Write out the sum. Do not evaluate.

- $$\sum _ { k = 1 } ^ { 5 } \frac { k + 1 } { k + 2 }$$

A) $\frac { 1 } { 3 } + \frac { 2 } { 4 } + \frac { 3 } { 5 } + \frac { 4 } { 6 }$

B) $\frac { 6 } { 7 }$

C) $\frac { 2 } { 3 } + \frac { 3 } { 4 } + \frac { 4 } { 5 } + \frac { 5 } { 6 } + \frac { 6 } { 7 }$

D) $\frac { 1 } { 2 } + \frac { 2 } { 3 } + \frac { 3 } { 4 } + \frac { 4 } { 5 } + \frac { 5 } { 6 }$

Question 35

Write out the sum. Do not evaluate.

- $$\sum _ { k = 1 } ^ { 6 } ( 5 k - 3 )$$

A) $2 + 7 + 12 + 17 + 22 + 27 + \ldots$
B) $1 + 2 + 7 + 12 + 17 + 22$
C) 60
D) $2 + 7 + 12 + 17 + 22 + 27$

Question 36

The given pattern continues. Write down the nth term of the sequence suggested by the pattern.

-2 , 4 , 8 , 16 , 32 , ...

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

Question 37

Express the sum using summation notation.

-2 + 4 + 6 + ... + 14

A)
$\sum _ { k = 0 } ^ { 7 } 2 k$

B) $\sum _ { k = 1 } ^ { 7 } 2 k$

C) $\sum _ { k = 1 } ^ { 7 } k ^ { 2 }$

D)
$\sum _ { k = 1 } ^ { 7 } 2 k ^ { 2 }$

Question 38

Write out the sum. Do not evaluate.

- $$\sum _ { k = 1 } ^ { n } 2 ^ { k + 1 }$$

A) $2 ^ { 2 } + 2 ^ { 3 } + 2 ^ { 4 } + \ldots + 2 ^ { n + 1 }$
B) $2 + 2 ^ { 2 } + 2 ^ { 3 } + \ldots + 2 ^ { n + 1 }$
C) $2 + 2 ^ { 2 } + 2 ^ { 3 } + \ldots + 2 ^ { n }$
D) $2 ^ { 2 } + 2 ^ { 3 } + 2 ^ { 4 } + \ldots + 2 ^ { n }$

Question 39

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 n represents a 30-minute interval. Let $$\mathrm { a } _ { 1 } = 490$$ represent the initial
Number of bacteria present.

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

Question 40

The sequence is defined recursively. Write the first four terms.

- $$a _ { 1 } = 2 , a _ { 2 } = 5 \text { and } a _ { n } = a _ { n - 2 } - 3 a _ { n - 1 } \text { for } n \geq 3$$

A) 2, 5, -1, -16
B) 2, 5, -13, 44
C) 2, 5, 1, 2
D) 2, 5, 17, -46

Question 41

Express the sum using summation notation with a lower limit of summation not necessarily 1 and with k for the index of
summation.

-7 + 11 + 15 + 19 + ... + 47

A) $\sum _ { k = 0 } ^ { 32 } 7 + 4 k$
B) $\sum _ { k = 1 } ^ { 10 } 7 + 4 k$
C) $\sum _ { k = 1 } ^ { 10 } 7 k + 4$
D) $\sum _ { k = 0 } ^ { 10 } 7 + 4 k$

Question 42

Find the sum of the sequence.

- $$\sum _ { \mathrm { k } = 1 } ^ { 4 } \left( - \frac { 1 } { 2 } \right) ^ { \mathrm { k } }$$

A) $\frac { 5 } { 16 }$
B) $\frac { 15 } { 16 }$
C) $- \frac { 1 } { 16 }$
D) $- \frac { 5 } { 16 }$

Question 43

Express the sum using summation notation.

- $$\frac { 1 } { 4 } + \frac { 2 } { 5 } + \frac { 1 } { 2 } + \cdots + \frac { 4 } { 5 }$$

A)
$\sum _ { k = 1 } ^ { n } \frac { k } { k + 3 }$

B)
$\sum _ { k = 1 } ^ { 12 } \frac { k } { k + 3 }$

C)
$\sum _ { k = 0 } ^ { 12 } \frac { k } { k + 3 }$

D)
$\sum _ { k = 3 } ^ { 12 } \frac { k } { k + 1 }$

Question 44

Express the sum using summation notation.

- $$\frac { 5 ^ { 14 } } { 9 ^ { 4 } } + \frac { 5 ^ { 13 } } { 9 ^ { 5 } } + \frac { 5 ^ { 12 } } { 9 ^ { 6 } } + \ldots + \frac { 5 ^ { 7 } } { 9 ^ { 11 } }$$

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 45

Express the sum using summation notation with a lower limit of summation not necessarily 1 and with k for the index of
summation.

- $$\frac { 4 } { 5 } + \frac { 5 } { 6 } + \frac { 6 } { 7 } + \frac { 7 } { 8 } + \ldots + \frac { 17 } { 18 }$$

A) $\sum _ { k = 5 } ^ { 17 } \frac { k } { k + 1 }$

B) $\sum _ { k = 4 } ^ { 17 } \frac { k + 1 } { k }$

C) $\sum _ { k = 4 } ^ { 17 } \frac { k } { k + 1 }$

D) $\sum _ { \mathrm { k } = 4 } ^ { 17 } \frac { \mathrm { k } } { \mathrm { k } \cdot 1.5 }$

Question 46

Find the sum of the sequence.

- $$\sum _ { k = 4 } ^ { 7 } 6 k$$

A) 132
B) 90
C) 42
D) 66

Question 47

Express the sum using summation notation.

- $$3 + 12 + 27 + \ldots + 75$$

A) $\sum _ { \mathrm { k } = 1 } ^ { 5 } 3 ^ { 2 } \mathrm { k }$

B) $\sum _ { \mathrm { k } = 0 } ^ { 5 } 3 \mathrm { k } ^ { 2 }$

C) $\sum _ { k = 1 } ^ { 5 } k ^ { 2 }$

D) $\sum _ { k = 1 } ^ { 5 } 3 k ^ { 2 }$

Question 48

Find the sum of the sequence.

- $$\sum _ { k = 1 } ^ { 5 } ( k + 1 )$$

A) 14
B) 20
C) 6
D) 8

Question 49

Express the sum using summation notation.

- $$\frac { 4 } { 5 } - \frac { 16 } { 25 } + \frac { 64 } { 125 } - \cdots + ( - 1 ) ^ { ( 13 + 1 ) } \left( \frac { 4 } { 5 } \right) ^ { 13 }$$

A)
$$\sum _ { k = 1 } ^ { n } ( - 1 ) ^ { ( k + 1 ) } \left( \frac { 4 } { 5 } \right) ^ { k }$$
B)
$$\sum _ { k = 1 } ^ { 14 } ( - 1 ) ^ { ( k + 1 ) } \left( \frac { 4 } { 5 } \right) ^ { k }$$
C)
$$\sum _ { k = 1 } ^ { 13 } ( - 1 ) ^ { ( k + 1 ) } \left( \frac { 4 } { 5 } \right) ^ { k }$$

D)
$\sum _ { k = 1 } ^ { 13 } \left( \frac { 4 } { 5 } \right) ^ { k }$

Question 50

Find the sum of the sequence.

- $$\sum _ { k = 1 } ^ { 4 } 3 ^ { k }$$

A) 39
B) 30
C) 84
D) 120

Question 51

Express the sum using summation notation.

- $$\frac { 1 } { w } + \frac { s } { 2 w } + \frac { s ^ { 2 } } { 3 w } + \ldots + \frac { s ^ { n - 1 } } { n w }$$

A) $\sum _ { \mathrm { k } = 1 } ^ { \mathrm { n } } \frac { \mathrm { s } ^ { \mathrm { k } } } { \mathrm { kw } }$

B) $\sum _ { k = 1 } ^ { n } \frac { s ^ { k - 1 } } { k w }$

C) $\sum _ { k = 0 } ^ { n } \frac { < b > k } { k w }$

D) $\sum _ { \mathrm { k } = 0 } ^ { \mathrm { n } } \frac { \mathrm { s } ^ { \mathrm { k } - 1 } } { \mathrm { kw } }$

Question 52

Find the sum of the sequence.

- $$\sum _ { k = 2 } ^ { 4 } k ( k + 5 )$$

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

Question 53

Find the sum of the sequence.

- $$\sum _ { k = 1 } ^ { 4 } ( - k )$$

A) -12
B) -4
C) -3
D) -10

Question 54

Find the sum of the sequence.

- $$\sum _ { k = 3 } ^ { 5 } \left( k ^ { 2 } - 9 \right)$$

A) -15
B) 23
C) 10
D) -3

Question 55

Find the sum of the sequence.

- $$\sum _ { k = 1 } ^ { 16 } ( 2 k + 7 )$$

A) 400
B) 384
C) 53
D) 272

Question 56

Express the sum using summation notation.

- $$4 ^ { 2 } + 8 ^ { 3 } + 12 ^ { 4 } + \ldots + 32 ^ { 9 }$$

A) $\sum _ { \mathrm { k } = 1 } ^ { 8 } 4 \mathrm { k } ^ { 2 \mathrm { k } - 1 }$
B) $\sum _ { k = 1 } ^ { 8 } ( 4 k ) ^ { k }$
C) $\sum _ { k = 1 } ^ { 8 } 2 ( k - 1 ) ^ { \mathrm { k } + 1 }$
D) $\sum _ { k = 1 } ^ { 8 } ( 4 k ) ^ { k + 1 }$

Question 57

Express the sum using summation notation with a lower limit of summation not necessarily 1 and with k for the index of
summation.

- $$4 + \frac { 9 } { 2 } + 5 + \frac { 11 } { 2 } + \ldots + \frac { 15 } { 2 }$$

A) $\sum _ { k = 8 } ^ { 15 } \frac { k } { 2 }$

B) $\sum _ { k = 8 } ^ { 12 } \frac { \mathrm { k } } { 2 }$

C) $\sum _ { \mathrm { k } = 1 } ^ { 15 } \frac { \mathrm { k } } { 2 }$

D) $\sum _ { k = 2 } ^ { 15 } \frac { \mathrm { k } } { 2 }$

Question 58

Express the sum using summation notation with a lower limit of summation not necessarily 1 and with k for the index of
summation.

-13 + 16 + 19 + 22 + ... + 37

A) $\sum _ { k = 1 } ^ { 10 } 7 + 3 k$

B) $\sum _ { k = 0 } ^ { 24 } 7 + 3 k$

C) $\sum _ { k = 2 } ^ { 24 } 7 + 3 k$

D) $\sum _ { k = 2 } ^ { 10 } 7 + 3 k$

Question 59

Find the sum of the sequence.

- $$\sum _ { k = 1 } ^ { 12 } 9$$

A) 9
B) 3
C) 108
D) 12

Question 60

Find the sum of the sequence.

- $$\sum _ { k = 2 } ^ { 5 } ( 4 k - 5 )$$

A) 36
B) 33
C) 23
D) 30

Question 61

Find the nth term and the indicated term of the arithmetic sequence whose initial term, a, and common difference, d, are
given.

- $$\begin{array} { l l } \mathrm { a } = 71 ; & \mathrm { d } = - 4 \\\mathrm { a } _ { \mathrm { n } } = ? ; & \mathrm { a } _ { 6 } = ?\end{array}$$

A) $a _ { n } = 75 - 4 n ; a _ { 6 } = 23$
B) $a _ { n } = 75 - 4 n ; a _ { 6 } = 51$
C) $a _ { n } = 71 - 4 n ; a _ { 6 } = 51$
D) $a _ { n } = 71 - 4 n ; a _ { 6 } = 23$

Question 62

Find the nth term and the indicated term of the arithmetic sequence whose initial term, a, and common difference, d, are
given.

- $$\begin{array} { l } \mathrm { a } = 9 ; \mathrm { d } = - 9 \\\mathrm { a } _ { \mathrm { n } } = ? ; \mathrm { a } _ { 13 } = ?\end{array}$$

A) $a _ { n } = 18 - 9 n ; a _ { 13 } = - 99$
B) $a _ { n } = 18 - 9 n ; a _ { 13 } = - 54$
C) $a _ { n } = 9 - 9 n ; a _ { 13 } = - 99$
D) $a _ { n } = 18 + 9 n ; a _ { 13 } = - 99$

Question 63

Determine whether the sequence is arithmetic.
4, 12, 36, 108, 972, ...

A) Arithmetic
B) Not arithmetic

Question 64

Determine whether the sequence is arithmetic.
-1, 1, 3, 5, 7, ...

A) Arithmetic
B) Not arithmetic

Question 65

Find the sum of the sequence.

- $$\sum _ { \mathrm { k } = 5 } ^ { 8 } \frac { 1 } { \mathrm { k } + 4 }$$

A) $- \frac { 197 } { 210 }$

B) $\frac { 624 } { 625 }$

C) 42

D) $\frac { 763 } { 1980 }$

Question 66

Solve.
A town has a population of 20,000 people and is increasing by 10% every year. What will the population be at the end of 4 years?

A) 26,620 people
B) 28,000 people
C) 9,282 people
D) 29,282 people

Question 67

An arithmetic sequence is given. Find the common difference and write out the first four terms.
{3n + 2}

A) d = 2; 3, 5, 8, 11
B) d = 3; 5, 8, 11, 14
C) d = 3; 3, 5, 8, 11
D) d = 2; 5, 8, 11, 14

Question 68

Find the sum of the sequence.

- $$\sum _ { k = 2 } ^ { 5 } ( - 1 ) ^ { k + 1 } ( k - 9 ) ^ { 2 }$$

A) -1,914
B) 126
C) -22
D) -126

Question 69

Find the sum of the sequence.

- $$\sum _ { k = 2 } ^ { 5 } \frac { - 3 } { k }$$

A) $- \frac { 77 } { 20 }$

B) $- \frac { 45 } { 16 }$

C) $\frac { 447 } { 10 }$

D) $\frac { 17 } { 20 }$

Question 70

Find the sum of the sequence.

- $$\sum _ { k = 1 } ^ { 4 } \frac { 1 } { 3 k }$$

A) $\frac { 11 } { 18 }$

B) $\frac { 5 } { 12 }$

C) $\frac { 25 } { 36 }$

D) $\frac { 1 } { 12 }$

Question 71

Solve.

-The number of students in a school in year n is estimated by the model $$a _ { n } = 7 n ^ { 2 } + 13 n + 81$$ . About how many students are in the school in each of the first three years?

A) 108, 135, 183
B) 101, 135, 162
C) 101, 135, 183
D) 114, 148, 196

Question 72

Determine whether the sequence is arithmetic.
2, 4, 6, 10, 12, ...

A) Arithmetic
B) Not arithmetic

Question 73

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

A) Arithmetic
B) Not arithmetic

Question 74

Find the sum of the sequence.

- $$\sum _ { k = 1 } ^ { 4 } ( - 1 ) ^ { k \cdot - 8 k }$$

A) -16
B) -80
C) 80
D) 4,096

Question 75

An arithmetic sequence is given. Find the common difference and write out the first four terms.
{9 - 6n}

A) d = 2; 4, 6 , 8 , 10
B) d = -6; 3, -3, -9, -15
C) d = -6; 3, -1 , -7 , -13
D) d = -6; -6, -12, -18, -24

Question 76

An arithmetic sequence is given. Find the common difference and write out the first four terms.

- $$\left\{ \frac { 1 } { 3 } + \frac { n } { 8 } \right\}$$

A) $\mathrm { d } = \frac { 1 } { 3 } ; \frac { 11 } { 24 } , \frac { 7 } { 12 } , \frac { 17 } { 24 } , \frac { 5 } { 6 }$

B) $\mathrm { d } = \frac { 1 } { 3 } ; \frac { 1 } { 3 } , \frac { 11 } { 24 } , \frac { 7 } { 12 } , \frac { 17 } { 24 }$

C) $\mathrm { d } = \frac { 1 } { 8 } ; \frac { 11 } { 24 } , \frac { 7 } { 12 } , \frac { 17 } { 24 } , \frac { 5 } { 6 }$

D) $\mathrm { d } = \frac { 1 } { 8 } ; \frac { 1 } { 3 } , \frac { 11 } { 24 } , \frac { 7 } { 12 } , \frac { 17 } { 24 }$

Question 77

Find the sum of the sequence.

- $$\sum _ { k = 1 } ^ { 4 } ( - 1 ) ^ { k } ( k + 6 )$$

A) 2
B) 34
C) -34
D) 26

Question 78

Determine whether the sequence is arithmetic.
2, -1, -4, -7, -10, ...

A) Arithmetic
B) Not arithmetic

Question 79

Find the nth term and the indicated term of the arithmetic sequence whose initial term, a, and common difference, d, are
given.

- $$\begin{array} { l } \mathrm { a } = 9 ; \mathrm { d } = 4 \\\mathrm { a } _ { \mathrm { n } } = ? ; \mathrm { a } _ { 14 } = ?\end{array}$$

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 80

Determine whether the sequence is arithmetic.
2, -3, -8, -13, -18, ...

A) Arithmetic
B) Not arithmetic