Deck 11: Sequences, Induction, and Probability

Question 1

Write the first four terms of the sequence whose general term is given.
$$a _ { n } = 4 ^ { n }$$

A) $4,16,64,256$
B) $1,16,81,256$
C) $1,4,16,64$
D) $16,64,256,1024$

Answer 1

A

Question 2

Write the first four terms of the sequence whose general term is given.
$$\mathrm { a } _ { \mathrm { n } } = \frac { ( - 1 ) ^ { \mathrm { n } + 1 } } { \mathrm { n } + 7 }$$

A) $\frac { 1 } { 8 } , - \frac { 1 } { 9 } , \frac { 1 } { 10 } , - \frac { 1 } { 11 }$
B) $- \frac { 1 } { 8 } , \frac { 1 } { 9 } , - \frac { 1 } { 10 } , \frac { 1 } { 11 }$
C) $\frac { 1 } { 8 } , - \frac { 1 } { 18 } , \frac { 1 } { 30 } , - \frac { 1 } { 44 }$
D) $- \frac { 1 } { 9 } , \frac { 1 } { 10 } , - \frac { 1 } { 11 } , \frac { 1 } { 12 }$

Answer 2

A

Question 3

Write the first four terms of the sequence whose general term is given.
$$\mathrm { a } _ { \mathrm { n } } = \mathrm { n } - 5$$

A) $- 4 , - 3 , - 2 , - 1$
B) $- 5 , - 4 , - 3 , - 2$
C) $0,1,2,3$
D) $- 20 , - 15 , - 10 , - 5$

Answer 3

A

Question 4

Write the first four terms of the sequence whose general term is given.
$$a _ { n } = 2 n$$

A) $2,4,6,8$
B) $0,2,4,6$
C) $3,4,5,6$
D) $1,0 , - 1 , - 2$

Question 5

Write the first four terms of the sequence whose general term is given.
$$a _ { n } = 4 n - 2$$

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

Question 6

Write the first four terms of the sequence whose general term is given.
$$a _ { n } = ( - 1 ) ^ { n + 1 } ( n + 8 )$$

A) $9 , - 10,11 , - 12$
В) $- 9,10 , - 11,12$
C) $9 , - 20,33 , - 48$
D) $- 10,11 , - 12,13$

Question 7

Write the first four terms of the sequence whose general term is given.
$$a _ { n } = 4 ( 3 n - 1 )$$

A) $8,20,32,44$
B) $2,5,8,11$
C) $- 4,8,20,32$
D) $8,16,24,32$

Question 8

Write the first four terms of the sequence whose general term is given.
$$a _ { n } = \left( \frac { 1 } { 3 } \right) ^ { n }$$

A) $\frac { 1 } { 3 } , \frac { 1 } { 9 } , \frac { 1 } { 27 } , \frac { 1 } { 81 }$
B) $1 , \frac { 1 } { 3 } , \frac { 1 } { 9 } , \frac { 1 } { 27 }$
C) $\frac { 1 } { 3 } , \frac { 1 } { 6 } , \frac { 1 } { 9 } , \frac { 1 } { 12 }$
D) $1 , \frac { 1 } { 9 } , \frac { 1 } { 27 } , \frac { 1 } { 81 }$

Question 9

Write the first four terms of the sequence whose general term is given.
A deposit of $\$ 11,000$ is made in an account that earns $5.6 \%$ interest compounded quarterly. The balance in the account after $n$ quarters is given by the sequence
$$a _ { n } = 11,000 \left( 1 + \frac { 0.056 } { 4 } \right) ^ { n } , n = 1,2,3 , \ldots$$
Find the balance in the account after 4 years.

A) $\$ 13,740.42$
B) $\$ 4996.52$
C) $\$ 11,629.06$
D) $\$ 3762.52$

Question 10

Write the first four terms of the sequence whose general term is given.
A deposit of $\$ 8000$ is made in an account that earns $8 \%$ interest compounded quarterly. The balance in the account after $n$ quarters is given by the sequence
$a _ { n } = 8000 \left( 1 + \frac { 0.08 } { 4 } \right) ^ { n } \quad n = 1,2,3 , \ldots$
Find the balance in the account after 28 quarters.

A) $\$ 13,928.19$
B) $\$ 14,014.19$
C) $\$ 13,989.19$
D) $\$ 13,781.19$

Question 11

Write the first four terms of the sequence whose general term is given.
$$a _ { n } = \left( - \frac { 1 } { 5 } \right) ^ { n }$$

A) $- \frac { 1 } { 5 } , \frac { 1 } { 25 } , - \frac { 1 } { 125 } , \frac { 1 } { 625 }$
B) $- \frac { 1 } { 5 } , - \frac { 1 } { 25 } , - \frac { 1 } { 125 } , - \frac { 1 } { 625 }$
C) $- \frac { 1 } { 5 } , \frac { 1 } { 10 } , - \frac { 1 } { 15 } , - \frac { 1 } { 20 }$
D) $\frac { 1 } { 5 } , - \frac { 1 } { 10 } , \frac { 1 } { 15 } , - \frac { 1 } { 20 }$

Question 12

Use Recursion Formulas
$a _ { 1 } = - 4$ and $a _ { n } = a _ { n - 1 } - 1$ for $n \geq 2$

A) $- 4 , - 5 , - 6 , - 7$
B) $4,3,2,1$
C) $4,5,6,7$
D) $- 4 , - 5 , - 4 , - 3$

Question 13

Write the first four terms of the sequence whose general term is given.
$$\mathrm { a } _ { \mathrm { n } } = ( - 2 ) ^ { \mathrm { n } }$$

A) $- 2,4 , - 8,16$
B) $- 2 , - 4 , - 8 , - 16$
C) $2 , - 4 , - 8 , - 16$
D) $2 , - 4,8 , - 16$

Question 14

Use Recursion Formulas
$a _ { 1 } = 3$ and $a _ { n } = a _ { n - 1 } - 5$ for $n \geq 2$

A) $3 , - 2 , - 7 , - 12$
B) $- 5 , - 10 , - 15 , - 20$
C) $3,8,13,18$
D) $3,0 , - 5 , - 10$

Question 15

Use Recursion Formulas
$a _ { 1 } = - 6$ and $a _ { n } = - 4 a _ { n - 1 }$ for $n \geq 2$

A) $- 6,24 , - 96,384$
B) $6 , - 24,96 , - 384$
C) $- 6 , - 24 , - 96 , - 384$
D) $- 6,26 , - 98,386$

Question 16

Write the first four terms of the sequence whose general term is given.
A deposit of $\$ 6000$ is made in an account that earns $9 \%$ interest compounded quarterly. The balance in the account after $n$ quarters is given by the sequence
$a _ { n } = 6000 \left( 1 + \frac { 0.09 } { 4 } \right) ^ { n } \quad n = 1,2,3 , \ldots$
Find the balance in the account after 7 years.

A) $\$ 11,187.27$
B) $\$ 11,263.27$
C) $\$ 11,242.27$
D) $\$ 11,056.27$

Question 17

Use Recursion Formulas
$a _ { 1 } = 5$ and $a _ { n } = 4 a _ { n - 1 }$ for $n \geq 2$

A) $5,20,80,320$
B) $5,19,18,17$
C) $16,64,256,512$
D) $5,22,82,322$

Question 18

Write the first four terms of the sequence whose general term is given.
$$a _ { n } = ( - 1 ) ^ { n } ( n + 5 )$$

A) $- 6,7 , - 8,9$
B) $- 6 , - 7 , - 8 , - 9$
C) $- 6 , - 14 , - 24 , - 36$
D) $6,7,8,9$

Question 19

Write the first four terms of the sequence whose general term is given.
$$a _ { n } = \frac { 4 } { n ^ { 2 } }$$

A) $4 , \frac { 4 } { 4 } , \frac { 4 } { 9 } , \frac { 4 } { 16 }$
B) $1 , \frac { 2 } { 4 } , \frac { 3 } { 9 } , \frac { 4 } { 16 }$
C) $\frac { 4 } { 4 } , \frac { 4 } { 9 } , \frac { 4 } { 16 } , \frac { 4 } { 25 }$
D) $1 , \frac { 1 } { 4 } , \frac { 1 } { 9 } , \frac { 1 } { 16 }$

Question 20

Write the first four terms of the sequence whose general term is given.
$$a _ { n } = \frac { n + 1 } { 2 n - 1 }$$

A) $2,1 , \frac { 4 } { 5 } , \frac { 5 } { 7 }$
B) $2 , - 1 , \frac { 4 } { 5 } , \frac { 5 } { 7 }$
C) $- 2,1 , \frac { 4 } { 5 } , \frac { 5 } { 7 }$
D) $- 2 , - 1 , \frac { 4 } { 5 } , \frac { 5 } { 7 }$

Question 21

Use Factorial Notation
$\frac { 7 ! } { 5 ! }$

A) 42
B) $2 !$
C) $\frac { 7 } { 5 }$
D) 7

Question 22

Use Factorial Notation
$\frac { 5 ! } { 7 ! }$

A) $\frac { 1 } { 42 }$
B) 42
C) 2 !
D) $\frac { 1 } { 2 ! }$

Question 23

Use Factorial Notation
$$a _ { n } = \frac { 3 ^ { n } } { ( n + 2 ) ! }$$

A) $\frac { 1 } { 2 } , \frac { 3 } { 8 } , \frac { 9 } { 40 } , \frac { 9 } { 80 }$
B) $1 , \frac { 9 } { 4 } , \frac { 27 } { 5 } , \frac { 27 } { 2 }$
C) $1 , \frac { 9 } { 4 } , \frac { 27 } { 5 } , \frac { 2 } { 27 }$
D) $\frac { 1 } { 2 } , \frac { 3 } { 8 } , \frac { 9 } { 20 } , \frac { 9 } { 40 }$

Question 24

Use Summation Notation
$$\sum _ { i = 1 } ^ { 4 } 2 ^ { i }$$

A) 30
B) 18
C) 14
D) 20

Question 25

Use Factorial Notation
$\frac { 10 ! } { 8 ! 2 ! }$

A) 45
B) 10
C) 0 !
D) 1

Question 26

Use Summation Notation
$$\sum _ { i = 9 } ^ { 12 } \frac { 1 } { i - 3 }$$

A) $\frac { 275 } { 504 }$
B) $\frac { 323 } { 660 }$
C) $- \frac { 820 } { 2187 }$
D) 30

Question 27

Use Summation Notation
$$\sum _ { i = 1 } ^ { 5 } ( i - 4 )$$

A) $- 5$
B) 1
C) $- 2$
D) $- 6$ )

Question 28

Use Summation Notation
$$\sum _ { i = 3 } ^ { 6 } ( 2 i - 2 )$$

A) 28
B) 24
C) 30
D) 16

Question 29

Use Factorial Notation
$$\frac { n ( n + 5 ) ! } { ( n + 6 ) ! }$$

A) $\frac { n } { n + 6 }$
B) $\frac { n } { 6 }$
C) $\frac { 1 } { n + 6 }$
D) $\frac { n } { ( n + 6 ) ! }$

Question 30

Use Summation Notation
$$\sum _ { i = 3 } ^ { 5 } \left( i ^ { 2 } - 8 \right)$$

A) 26
B) 15
C) 0
D) $- 12$

Question 31

Use Summation Notation
$$\sum _ { i = 1 } ^ { 4 } \frac { 1 } { 8 i }$$

A) $\frac { 25 } { 96 }$
B) $\frac { 1 } { 32 }$
C) $\frac { 5 } { 32 }$
D) $\frac { 11 } { 48 }$

Question 32

Use Summation Notation
$\sum _ { i = 4 } ^ { 7 } 9 i$

A) 198
B) 63
C) 99
D) 135

Question 33

Use Recursion Formulas
$a _ { 1 } = 3$ and $a _ { n } = 2 a _ { n - 1 } - 4$ for $n \geq 2$

A) $3,2,0 , - 4$
B) $3,2,8,20$
C) $3,6,12,24$
D) $3,10,24,52$

Question 34

Use Factorial Notation
$$a _ { n } = \frac { 4 ( n + 1 ) ! } { n ! }$$

A) $8,12,16,20$
B) $8,6 , \frac { 8 } { 3 } , \frac { 5 } { 6 }$
C) $5,6,7,8$
D) $8,6 , \frac { 16 } { 3 } , 5$ Evaluate the factorial expression.

Question 35

Use Factorial Notation
$$a _ { n } = \frac { n ^ { 2 } } { ( n + 1 ) ! }$$

A) $\frac { 1 } { 2 } , \frac { 2 } { 3 } , \frac { 3 } { 8 } , \frac { 2 } { 15 }$
B) $1 , \frac { 2 } { 3 } , \frac { 1 } { 4 } , \frac { 1 } { 15 }$
C) $\frac { 1 } { 2 } , \frac { 2 } { 3 } , \frac { 3 } { 4 } , \frac { 4 } { 5 }$
D) $1 , \frac { 2 } { 3 } , \frac { 1 } { 2 } , \frac { 2 } { 5 }$

Question 36

Use Factorial Notation
$$a _ { n } = \frac { ( n + 1 ) ! } { n ^ { 4 } }$$

A) $2 , \frac { 3 } { 8 } , \frac { 8 } { 27 } , \frac { 15 } { 32 }$
B) $\frac { 1 } { 2 } , \frac { 3 } { 4 } , 2 , \frac { 15 } { 2 }$
C) $2 , \frac { 3 } { 8 } , \frac { 4 } { 27 } , \frac { 5 } { 64 }$
D) $\frac { 1 } { 2 } , \frac { 3 } { 4 } , 1 , \frac { 5 } { 4 }$

Question 37

Use Factorial Notation
$\frac { 8 ! } { 7 ! }$

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

Question 38

Use Factorial Notation
$$a _ { n } = 3 ( n + 2 ) !$$

A) $18,72,360,2160$
B) $18,144,1080,8640$
C) $6,36,216,1440$
D) $6,18,72,360$

Question 39

Use Factorial Notation
$$\frac { ( n + 6 ) ! } { n + 6 }$$

A) $( n + 5 ) !$
B) 1
C) $6 !$
D) $n + 6 !$

Question 40

Use Factorial Notation
$\frac { 10 ! } { 5 ! 5 ! }$

A) 252
B) 504
C) 30,240
D) 126

Question 41

Express the sum using summation notation. Use a lower limit of summation not necessarily 1 and k for the index of summation.
$11 + 14 + 17 + 20 + \ldots + 35$

A) $\sum _ { \mathrm { k } = 2 } ^ { 10 } 3 \mathrm { k } + 5$
B) $\sum _ { k = 0 } ^ { 24 } 3 k + 5$
C) $\sum _ { \mathrm { k } = 1 } ^ { 10 } 3 \mathrm { k } + 5$
D) $\sum _ { k = 2 } ^ { 24 } 3 k + 5$

Question 42

Use Summation Notation
$$\sum _ { \mathrm { i } = 1 } ^ { 5 } \frac { ( - 1 ) ^ { \mathrm { i } + 1 } } { ( \mathrm { i } + 1 ) ! }$$

A) $\frac { 53 } { 144 }$
B) $- \frac { 53 } { 144 }$
C) $\frac { 23 } { 60 }$
D) $- \frac { 23 } { 60 }$

Question 43

Use Summation Notation
$$\sum _ { i = 2 } ^ { 5 } 11$$

A) 44
B) 154
C) 33
D) 132

Question 44

Use Summation Notation
$$\sum _ { k = 2 } ^ { 4 } k ( k - 4 )$$

A) $- 7$
B) $- 10$
C) $- 4$
D) 6

Question 45

Express the sum using summation notation. Use a lower limit of summation not necessarily 1 and k for the index of summation.
$$4 + \frac { 9 } { 2 } + 5 + \frac { 11 } { 2 } + \ldots + 9$$

A) $\sum _ { \mathrm { k } = 8 } ^ { 18 } \frac { \mathrm { k } } { 2 }$
B) $\sum _ { \mathrm { k } = 1 } ^ { 18 } \frac { \mathrm { k } } { 2 }$
C) $\sum _ { \mathrm { k } = 8 } ^ { 12 } \frac { \mathrm { k } } { 2 }$
D) $\sum _ { \mathrm { k } = 2 } ^ { 18 } \frac { \mathrm { k } } { 2 }$

Question 46

Express the sum using summation notation. Use 1 as the lower limit of summation and i for the index of summation.
$$3 + 6 + 9 + \ldots + 27$$

A) $\sum _ { i = 1 } ^ { 9 } 3 \mathrm { i }$
B) $\sum _ { i = 0 } ^ { 9 } 3 i$
C) $\sum _ { i = 1 } ^ { 9 } i ^ { 2 }$
D) $\sum _ { i = 1 } ^ { 9 } 3 \mathrm { i } ^ { 2 }$

Question 47

Express the sum using summation notation. Use 1 as the lower limit of summation and i for the index of summation.
$$\frac { 1 } { 3 } + \frac { 1 } { 2 } + \frac { 3 } { 5 } + \ldots + \frac { 7 } { 8 }$$

A) $\sum _ { i = 1 } ^ { 14 } \frac { i } { i + 2 }$
B) $\sum _ { i = 0 } ^ { 14 } \frac { \mathrm { i } } { \mathrm { i } + 2 }$
C) $\sum _ { i = 1 } ^ { n } \frac { i } { i + 2 }$
D) $\sum _ { i = 2 } ^ { 14 } \frac { \mathrm { i } } { \mathrm { i } + 1 }$

Question 48

Use Summation Notation
$$\sum _ { i = 3 } ^ { 6 } \frac { i ! } { ( i - 1 ) ! }$$

A) 18
B) 10
C) 3
D) 6

Question 49

Express the sum using summation notation. Use a lower limit of summation not necessarily 1 and k for the index of summation.
$$5 + 6 + 7 + 8 + \ldots + 22$$

A) $\sum _ { \mathrm { k } = 7 } ^ { 24 } ( \mathrm { k } - 2 )$
B) $\sum _ { k = 5 } ^ { 22 } ( k - 2 )$
C) $\sum _ { k = 3 } ^ { 20 } ( \mathrm { k } - 2 )$
D) $\sum _ { k = 1 } ^ { 17 } ( \mathrm { k } - 2 )$

Question 50

Use Summation Notation
$$\sum _ { k = 1 } ^ { 4 } ( - 1 ) ^ { k } ( k + 4 )$$

A) 2
B) $- 26$
C) 26
D) 18

Question 51

Express the sum using summation notation. Use a lower limit of summation not necessarily 1 and k for the index of summation.
$$( a + 1 ) + ( a + d ) + \left( a + d ^ { 2 } \right) + \ldots + \left( a + d ^ { n } \right)$$

A) $\sum _ { \mathrm { k } = 0 } ^ { \mathrm { n } } \left( \mathrm { a } + \mathrm { d } ^ { \mathrm { k } } \right)$
B) $\sum _ { k = 1 } ^ { n } \left( a + d ^ { k } \right)$
C) $\sum _ { k = 0 } ^ { n - 1 } \left( a + d ^ { k } \right)$
D) $\sum _ { \mathrm { k } = 0 } ^ { \mathrm { n } } \mathrm { ad } ^ { \mathrm { k } }$

Question 52

Express the sum using summation notation. Use a lower limit of summation not necessarily 1 and k for the index of summation.
$$\frac { 3 } { 4 } + \frac { 4 } { 5 } + \frac { 5 } { 6 } + \frac { 6 } { 7 } + \ldots + \frac { 17 } { 18 }$$

A) $\sum _ { k = 3 } ^ { 17 } \frac { k } { k + 1 }$
B) $\sum _ { k = 4 } ^ { 17 } \frac { \mathrm { k } + 1 } { \mathrm { k } }$
C) $\sum _ { \mathrm { k } = 3 } ^ { 17 } \frac { \mathrm { k } + 1 } { \mathrm { k } }$
D) $\sum _ { k = 4 } ^ { 17 } \frac { \mathrm { k } } { \mathrm { k } + 1 }$

Question 53

Express the sum using summation notation. Use a lower limit of summation not necessarily 1 and k for the index of summation.
$$a + a r + a r ^ { 2 } + \ldots + a r ^ { 11 }$$

A) $\sum _ { \mathrm { k } = 0 } ^ { 11 } \mathrm { ar } ^ { \mathrm { k } }$
B) $\sum _ { k = 1 } ^ { 12 } a r ^ { k }$
C) $\sum _ { \mathrm { k } = 0 } ^ { 11 } ( \mathrm { ar } ) ^ { \mathrm { k } }$
D) $\sum _ { k = 1 } ^ { 11 } a r ^ { k }$

Question 54

Express the sum using summation notation. Use 1 as the lower limit of summation and i for the index of summation.
$$2 + 8 + 18 + \ldots + 50$$

A) $\sum _ { i = 1 } ^ { 5 } 2 i ^ { 2 }$
B) $\sum _ { i = 0 } ^ { 5 } 2 i ^ { 2 }$
C) $\sum _ { i = 1 } ^ { 5 } i ^ { 2 }$
D) $\sum _ { i = 1 } ^ { 5 } 2 ^ { 2 }$

Question 55

Express the sum using summation notation. Use a lower limit of summation not necessarily 1 and k for the index of summation.
The bar graph below shows a company's yearly profits from 1991 to 1999. Let an represent the company's profit, in millions, in year $\mathrm { n }$ , where $\mathrm { n } = 1$ corresponds to $1991 , \mathrm { n } = 2$ corresponds to 1992 , and so on.
Find $\sum _ { i = 3 } ^ { 7 } a _ { i }$

A) \$356.9 million
B) \$400.7 million
C) $\$ 142.6$ million
D) $\$ 371.3$ million

Question 56

Use Summation Notation
$$\sum _ { i = 1 } ^ { 4 } \left( - \frac { 1 } { 4 } \right) ^ { i }$$

A) $- \frac { 51 } { 256 }$
B) $\frac { 51 } { 256 }$
C) $- \frac { 47 } { 256 }$
D) $\frac { 85 } { 256 }$

Question 57

Use Summation Notation
$$\sum _ { \mathrm { i } = 1 } ^ { 5 } \frac { ( \mathrm { i } - 1 ) ! } { ( \mathrm { i } + 2 ) ! }$$

A) $\frac { 5 } { 21 }$
B) $\frac { 241 } { 140 }$
C) $\frac { 37 } { 30 }$
D) $\frac { 43 } { 20 }$

Question 58

Express the sum using summation notation. Use 1 as the lower limit of summation and i for the index of summation.
$$a + a r + a r ^ { 2 } + \ldots + a r ^ { 13 }$$

A) $\sum _ { i = 1 } ^ { 14 } a r ^ { i - 1}$
B) $\sum _ { \mathrm { i } = 1 } ^ { 13 } a r ^ { \mathrm { i } }$
C) $\sum _ { i = 1 } ^ { 13 } ( a r ) ^ { i }$
D) $\sum _ { i = 1 } ^ { 13 } ( \operatorname { ar } ) ^ { i - 1 }$

Question 59

Express the sum using summation notation. Use 1 as the lower limit of summation and i for the index of summation.
$$a + 1 + \frac { a + 2 } { 2 } + \ldots + \frac { a + 6 } { 6 }$$

A) $\sum _ { i = 1 } ^ { 6 } \frac { a + i } { i }$
B) $\sum _ { i = 0 } ^ { 6 } \frac { a + i } { i }$
C) $\sum _ { i = 0 } ^ { n } \frac { a + i } { i }$
D) $\sum _ { i = 1 } ^ { n } \frac { a + i } { i }$

Question 60

Express the sum using summation notation. Use 1 as the lower limit of summation and i for the index of summation.
$$5 ^ { 2 } + 10 ^ { 3 } + 15 ^ { 4 } + \ldots + 40 ^ { 9 }$$

A) $\sum _ { \mathrm { i } = 1 } ^ { 8 } ( 5 \mathrm { i } ) ^ { \mathrm { i } + 1 }$
B) $\sum _ { i = 1 } ^ { 8 } ( 5 i ) ^ { i }$
C) $\sum _ { i = 1 } ^ { 8 } 2 ( i - 1 ) ^ { i + 1 }$
D) $\sum _ { i = 1 } ^ { 8 } 5 i ^ { 2 i - 1 }$

Question 61

Arithmetic Sequences
Find the Common Difference for an Arithmetic Sequence
$5,8,11,14 , \ldots$

A) 3
B) 9
C) $- 3$
D) $- 9$ )

Question 62

Use the Formula for the General Term of an Arithmetic Sequence
Choose the one alternative that best completes the statement or answers the question.
Use the formula for the general term (the nth term) of an arithmetic sequence to find the indicated term of the
sequence with the given first term, a1, and common difference, d.
Find $a 18$ when $a _ { 1 } = 10 , d = - 1$ .

A) $- 7$
B) $- 8$
C) 27
D) 28 8

Question 63

Write Terms of an Arithmetic Sequence
$$\mathrm { a } _ { \mathrm { n } } = \mathrm { a } _ { \mathrm { n } } - 1 + \frac { 1 } { 3 } ; \mathrm { a } _ { 1 } = \frac { 4 } { 9 }$$

A) $\frac { 4 } { 9 } , \frac { 7 } { 9 } , \frac { 10 } { 9 } , \frac { 13 } { 9 } , \frac { 16 } { 9 }$
B) $\frac { 4 } { 9 } , \frac { 1 } { 9 } , - \frac { 2 } { 9 } , - \frac { 5 } { 9 } , - \frac { 8 } { 9 }$
C) $\frac { 4 } { 9 } , \frac { 8 } { 9 } , \frac { 4 } { 3 } , \frac { 16 } { 9 } , \frac { 20 } { 9 }$
D) $\frac { 4 } { 9 } , \frac { 7 } { 9 } , \frac { 11 } { 9 } , \frac { 14 } { 9 } , \frac { 17 } { 9 }$

Question 64

Use the Formula for the General Term of an Arithmetic Sequence
Choose the one alternative that best completes the statement or answers the question.
Use the formula for the general term (the nth term) of an arithmetic sequence to find the indicated term of the
sequence with the given first term, a1, and common difference, d.
Find a 19 when $a _ { 1 } = - 4 , d = - \frac { 5 } { 3 }$ .

A) $- 34$
B) $- \frac { 107 } { 3 }$
C) 26
D) $\frac { 83 } { 3 }$

Question 65

Arithmetic Sequences
Find the Common Difference for an Arithmetic Sequence
$624,616,608,600 , \ldots$

A) $- 8$
B) 8
C) 624
D) $- 624$

Question 66

Write Terms of an Arithmetic Sequence
$$a _ { n } = a _ { n } - 1 + 6 ; a _ { 1 } = 3$$

A) $3,9,15,21,27$
B) $2,8,14,20,26$
C) $6,9,12,15,18$
D) $3,6,9,15,21$

Question 67

Write Terms of an Arithmetic Sequence
$$a _ { n } = a _ { n } - 1 - 2.2 ; a _ { 1 } = - 14$$

A) $- 14 , - 16.2 , - 18.4 , - 20.6 , - 22.8$
B) $- 15 , - 17.2 , - 19.4 , - 21.6 , - 23.8$
C) $- 2.2 , - 16.2 , - 30.2 , - 44.2 , - 58.2$
D) $- 14 , - 2.2 , - 16.2 , - 18.4 , - 20.6$

Question 68

Use the Formula for the General Term of an Arithmetic Sequence
Choose the one alternative that best completes the statement or answers the question.
Use the formula for the general term (the nth term) of an arithmetic sequence to find the indicated term of the
sequence with the given first term, a1, and common difference, d.
Find $a _ { 13 }$ when $a _ { 1 } = 20 , d = - 3$ .

A) $- 16$
B) $- 19$
C) $- 36$
D) 56

Question 69

Write Terms of an Arithmetic Sequence
$$\mathrm { a } _ { \mathrm { n } } = \mathrm { a } _ { \mathrm { n } } - 1 + 2 ; \mathrm { a } _ { 1 } = - 8$$

A) $- 8 , - 6 , - 4 , - 2,0$
B) $- 9 , - 7 , - 5 , - 3 , - 1$
C) $2 , - 6 , - 14 , - 22 , - 30$
D) $- 8,2 , - 6 , - 4 , - 2$

Question 70

Arithmetic Sequences
Find the Common Difference for an Arithmetic Sequence
$8,11,14,17 , \ldots$

A) 3
B) 9
C) $2.25$
D) 8

Question 71

Write Terms of an Arithmetic Sequence
$$\mathrm { a } _ { \mathrm { n } } = \mathrm { a } _ { \mathrm { n } } - 1 - 8 ; \mathrm { a } _ { 1 } = - 11$$

A) $- 11 , - 19 , - 27 , - 35 , - 43$
B) $- 12 , - 20 , - 28 , - 36 , - 44$
C) $- 8 , - 19 , - 30 , - 41 , - 52$
D) $- 11 , - 8 , - 19 , - 27 , - 35$

Question 72

Write Terms of an Arithmetic Sequence
$$a _ { 1 } = - 21 ; d = 4$$

A) $- 21 , - 17 , - 13 , - 9 , - 5$
B) $- 13 , - 9 , - 5 , - 1,3$
C) $- 5 , - 9 , - 13 , - 17 , - 21$
D) $- 13 , - 17 , - 21 , - 25 , - 29$

Question 73

Write Terms of an Arithmetic Sequence
$$a _ { 1 } = 14 ; d = - 3$$

A) $14,11,8,5,2$
B) $0,14,11,8,5$
C) $- 14 , - 11 , - 8 , - 5 , - 2$
D) $18,14,10,6,2$

Question 74

Write Terms of an Arithmetic Sequence
$$a _ { 1 } = 8 ; d = 3$$

A) $8,11,14,17,20$
B) $11,14,17,20,23$
C) $0,8,11,14,17$
D) $8,10,12,14,16$

Question 75

Write Terms of an Arithmetic Sequence
$$a _ { 1 } = - \frac { 5 } { 2 } , d = - \frac { 3 } { 2 }$$

A) $- \frac { 5 } { 2 } , - 4 , - \frac { 11 } { 2 } , - 7 , - \frac { 17 } { 2 }$
B) $- \frac { 5 } { 2 } , - 1 , \frac { 1 } { 2 } , 2 , \frac { 7 } { 2 }$
C) $- \frac { 5 } { 2 } , - 2 , - \frac { 11 } { 6 } , - \frac { 7 } { 4 } , - \frac { 17 } { 10 }$
D) $- \frac { 5 } { 2 } , - \frac { 1 } { 2 } , \frac { 1 } { 6 } , \frac { 1 } { 2 } , \frac { 7 } { 10 }$

Question 76

Write Terms of an Arithmetic Sequence
$$a _ { 1 } = 9 ; \mathrm { d } = - 2$$

A) $9,7,5,3,1$
B) $11,9,7,5,3$
C) $7,5,3,1 , - 1$
D) $9,7,4,3,1$

Question 77

Use the Formula for the General Term of an Arithmetic Sequence
Choose the one alternative that best completes the statement or answers the question.
Use the formula for the general term (the nth term) of an arithmetic sequence to find the indicated term of the
sequence with the given first term, a1, and common difference, d.
Find a8 when $a _ { 1 } = - 10 , d = - 4$ .

A) $- 38$
B) $- 42$
C) 18
D) 22

Question 78

Express the sum using summation notation. Use a lower limit of summation not necessarily 1 and k for the index of summation.
The finite sequence whose general term is
$$a _ { n } = 0.11 n ^ { 2 } - 1.06 n + 7.29$$
where $n = 1,2,3 , \ldots , 9$ models the total operating costs, in millions of dollars, for a company from 1991 through $1999 .$
Find $\sum _ { \mathrm { i } = 1 } ^ { 5 } \mathrm { a } _ { \mathrm { i } }$

A) $\$ 26.6$ million
B) \$31.7 million
C) \$21.86 million
D) $\$ 25.36$ million

Question 79

Write Terms of an Arithmetic Sequence
$$a _ { 1 } = - \frac { 3 } { 8 } ; d = - \frac { 1 } { 8 }$$

A) $- \frac { 3 } { 8 } , - \frac { 1 } { 2 } , - \frac { 5 } { 8 } , - \frac { 3 } { 4 } , - \frac { 7 } { 8 }$
B) $- \frac { 3 } { 8 } , - \frac { 1 } { 4 } , - \frac { 1 } { 8 } , 0 , \frac { 1 } { 8 }$
C) $- \frac { 3 } { 8 } , - \frac { 3 } { 4 } , - \frac { 9 } { 8 } , - \frac { 3 } { 2 } , - \frac { 15 } { 8 }$
D) $- \frac { 3 } { 8 } , - \frac { 1 } { 2 } , - \frac { 1 } { 8 } , - \frac { 3 } { 4 } , \frac { 1 } { 8 }$

Question 80

Arithmetic Sequences
Find the Common Difference for an Arithmetic Sequence
$$- 15 , - 17 , - 19 , - 21 , \ldots$$

A) $- 2$
B) -6
C) $- 4$
D) 6