Deck 8: Quadratic Equations and Functions

Question 1

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

A) $\frac { 3 } { 4 } , \frac { 9 } { 5 } , \frac { 9 } { 2 } , \frac { 81 } { 7 }$
B) $\frac { 1 } { 8 } , \frac { 3 } { 40 } , \frac { 3 } { 80 } , \frac { 9 } { 560 }$
C) $\frac { 3 } { 7 } , \frac { 9 } { 8 } , 3 , \frac { 81 } { 10 }$
D) $\frac { 1 } { 8 } , \frac { 3 } { 40 } , \frac { 3 } { 40 } , \frac { 9 } { 280 }$

Answer 1

B

Question 2

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

A) 1, 2, 3, 4
B) -1, -3, -5, -7
C) 3, 5, 7, 9
D) 1, 3, 5, 7

Answer 2

D

Question 3

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

A) $- \frac { 1 } { 10 } , \frac { 1 } { 11 } , - \frac { 1 } { 12 } , \frac { 1 } { 13 }$
B) $\frac { 1 } { 9 } , - \frac { 1 } { 20 } , \frac { 1 } { 33 } , - \frac { 1 } { 48 }$
C) $- \frac { 1 } { 9 } , \frac { 1 } { 10 } , - \frac { 1 } { 11 } , \frac { 1 } { 12 }$
D) $\frac { 1 } { 9 } , - \frac { 1 } { 10 } , \frac { 1 } { 11 } , - \frac { 1 } { 12 }$

Answer 3

D

Question 4

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

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

Question 5

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

A) $\frac { 1 } { 4 } , \frac { 1 } { 8 } , \frac { 1 } { 6 } , \frac { 3 } { 8 }$
B) $0,0 , \frac { 2 } { 81 } , \frac { 3 } { 128 }$
C) $0,0 , \frac { 1 } { 6 } , \frac { 3 } { 8 }$
D) $1 , \frac { 1 } { 16 } , \frac { 2 } { 81 } , \frac { 3 } { 128 }$

Question 6

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

A) $- 3 , \frac { 4 } { 3 } , 1 , \frac { 6 } { 7 }$
B) $3 , \frac { 4 } { 3 } , 1 , \frac { 6 } { 7 }$
C) $- 3 , - \frac { 4 } { 3 } , 1 , \frac { 6 } { 7 }$
D) $3 , - \frac { 4 } { 3 } , 1 , \frac { 6 } { 7 }$

Question 7

Write the first four terms of the sequence whose general term is given.
$$a _ { n } = ( - 1 ) ^ { n + 1 } ( n + 9 )$$

A) $- 10,11 , - 12,13$
B) $10 , - 22,36 , - 52$
C) $- 11,12 , - 13,14$
D) $10 , - 11,12 , - 13$

Question 8

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

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

Question 9

Write the first four terms of the sequence whose general term is given.
an = n2n+ 2

A) 1 3 2 5
B) 1 1 3 2
C) 1 1 3 2
D) 1 1 3 2 3 , 11 , 9 , 27 2 , 3 , 8 , 5 3 , 3 , 11 , 9 3 , 3 , 8 , 5

Question 10

Write the first four terms of the sequence whose general term is given.
$$\mathrm { a } _ { \mathrm { n } } = \left( \frac { 2 } { 3 } \right) ^ { \mathrm { n } }$$

A) $\frac { 2 } { 3 } , \frac { 4 } { 9 } , \frac { 8 } { 27 } , \frac { 16 } { 81 }$
B) $\frac { 2 } { 3 } , \frac { 2 } { 6 } , \frac { 2 } { 9 } , \frac { 2 } { 12 }$
C) $1 , \frac { 4 } { 9 } , \frac { 8 } { 27 } , \frac { 16 } { 81 }$
D) $1 , \frac { 2 } { 3 } , \frac { 4 } { 9 } , \frac { 8 } { 27 }$

Question 11

Solve the problem.
A deposit of $8000 is made in an account that earns 5.2% interest compounded quarterly. The balance in the account after n quarters is given by the sequence an = 8000(1 + 0.0524 )n, n = 1, 2, 3, ... Find the balance in the account after six years by computing a24

A) $8180.46
B) $10,907.29
C) $6946.46
D) $8644.63

Question 12

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

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

Question 13

Write the first four terms of the sequence whose general term is given.
$$a _ { n } = 2 ( 2 n - 3 )$$

A) -2, -4, -6, -8, -10
B) -2, 2, 6, 10, 14
C) -1, 1, 3, 5, 7
D) -6, -2, 2, 6, 10

Question 14

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

A) $- 8,48 , - 288,1920$
B) $- 8 , - 24 , - 96 , - 480$
C) $- 4 , - 16 , - 72 , - 384$
D) $- 4,8 , - 24,96$

Question 15

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

A) $- \frac { 3 } { 4 } , \frac { 9 } { 16 } , - \frac { 27 } { 64 } , \frac { 81 } { 256 }$
B) $- \frac { 3 } { 4 } , - \frac { 9 } { 16 } , - \frac { 27 } { 64 } , - \frac { 81 } { 256 }$
C) $\frac { 3 } { 4 } , - \frac { 3 } { 8 } , \frac { 3 } { 12 } , - \frac { 3 } { 16 }$
D) $- \frac { 3 } { 4 } , \frac { 3 } { 8 } , - \frac { 3 } { 12 } , - \frac { 3 } { 16 }$

Question 16

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

A) -4, -3, -2, -1
B) -16, -12, -8, -4
C) -3, -2, -1, 0
D) -1, 0, 1, 2

Question 17

Write the first four terms of the sequence whose general term is given.
$$a _ { n } = 3 ^ { n }$$

A) 9, 27, 81, 243
B) 1, 8, 27, 64
C) 1, 3, 9, 27
D) 3, 9, 27, 81

Question 18

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

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

Question 19

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

A) $3,4,5,6$
B) $- 3 , - 8 , - 15 , - 24$
C) $- 3,4 , - 5,6$
D) $- 3 , - 4 , - 5 , - 6$

Question 20

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

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

Question 21

Find the indicated sum.
$$\sum _ { i = 1 } ^ { 4 } 2 ^ { i }$$

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

Question 22

Express the sum using summation notation. Use 1 as the lower limit of summation and i for the index of summation.
$$6 ^ { 2 } + 12 ^ { 3 } + 18 ^ { 4 } + \ldots + 48 ^ { 9 }$$

A) $\sum _ { i = 1 } ^ { 8 } 6 i ^ { 2 i } - 1$
B) $\sum _ { i = 1 } ^ { 8 } ( 6 i ) ^ { i } + 1$
C) $\sum _ { \mathrm { i } = 1 } ^ { 8 } 2 ( \mathrm { i } - 1 ) ^ { \mathrm { i } + 1 }$
D) $\sum _ { \mathrm { i } = 1 } ^ { 8 } ( 6 \mathrm { i } ) ^ { \mathrm { i } }$

Question 23

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

A) $- 8 , - 6 , - \frac { 8 } { 3 } , - \frac { 5 } { 6 }$
B) $- 8 , - 6 , - \frac { 16 } { 3 } , - 5$
C) $- 8 , - 12 , - 16 , - 20$
D) $- 3 , - 2 , - 1,0$

Question 24

Find the indicated sum.
$$\sum _ { k = 2 } ^ { 4 } \mathrm { k } ( \mathrm { k } + 11 )$$

A) 86
B) 51
C) 140
D) 128

Question 25

Express the sum using summation notation. Use 1 as the lower limit of summation and i for the index of summation.
$$2 + 8 + 18 + \ldots + 72$$

A) $\sum _ { \mathrm { i } = 1 } ^ { 6 } 2 ^ { 2 } \mathrm { i }$
B) $\sum _ { \mathrm { i } = 1 } ^ { 6 } 2 \mathrm { i } ^ { 2 }$
C) $\sum _ { \mathrm { i } = 0 } ^ { 6 } 2 \mathrm { i } ^ { 2 }$
D) $\sum _ { i = 1 } ^ { 6 } i ^ { 2 }$

Question 26

Find the indicated sum.
$$\sum _ { i = 2 } ^ { 5 } ( 3 i - 2 )$$

A) 19
B) 26
C) 34
D) 30

Question 27

Find the indicated sum.
$$\sum _ { i = 3 } ^ { 8 } 12$$

A) 60
B) 396
C) 360
D) 72

Question 28

Find the indicated sum.
$$\sum _ { i = 1 } ^ { 5 } ( i - 10 )$$

A) $- 35$
B) $- 5$
C) $- 30$
D) $- 14$

Question 29

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

Question 30

Find the indicated sum.
$$\sum _ { i = 1 } ^ { 5 } \frac { ( - 1 ) ^ { \mathrm { i } + 1 } } { ( \mathrm { i } + 2 ) ! }$$

A) $\frac { 37 } { 280 }$
B) $- \frac { 109 } { 420 }$
C) $- \frac { 37 } { 280 }$
D) $\frac { 109 } { 420 }$

Question 31

Find the indicated sum.
$$\sum _ { i = 3 } ^ { 5 } \left( i ^ { 2 } - 5 \right)$$

A) 9
B) 35
C) 30
D) $- 3$

Question 32

Find the indicated sum.
$$\sum _ { i = 3 } ^ { 6 } \frac { i ! } { ( i - 1 ) ! }$$

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

Question 33

Express the sum using summation notation. Use 1 as the lower limit of summation and i for the index of summation.
$$\frac { 1 } { 3 } + \frac { 1 } { 2 } + \frac { 3 } { 5 } + \ldots + \frac { 6 } { 7 }$$

A) $\sum _ { i = 2 } ^ { 12 } \frac { i } { i + 1 }$
B) $\sum _ { i = 1 } ^ { n } \frac { i } { i + 2 }$
C) $\sum _ { i = 0 } ^ { 12 } \frac { i } { i + 2 }$
D) $\sum _ { i = 1 } ^ { 12 } \frac { i } { i + 2 }$

Question 34

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

Question 35

Find the indicated sum.
$\sum _ { i = 4 } ^ { 7 } 8 i$

A) 176
B) 120
C) 88
D) 56

Question 36

Find the indicated sum.
$$\sum _ { i = 1 } ^ { 5 } \frac { ( \mathrm { i } - 1 ) ! } { ( \mathrm { i } + 1 ) ! }$$

A) $\frac { 9 } { 5 }$
B) $\frac { 5 } { 6 }$
C) $\frac { 21 } { 10 }$
D) $\frac { 73 } { 30 }$

Question 37

Find the indicated sum.
$$\sum _ { k = 1 } ^ { 4 } ( - 1 ) ^ { k } ( k + 13 )$$

A) 54
B) 2
C) $- 62$
D) 62

Question 38

Find the indicated sum.
$$\sum _ { i = 1 } ^ { 4 } \frac { 1 } { 6 i }$$

A) $\frac { 1 } { 24 }$
B) $\frac { 11 } { 36 }$
C) $\frac { 25 } { 72 }$
D) $\frac { 5 } { 24 }$

Question 39

Find the indicated sum.
$$\sum _ { i = 6 } ^ { 9 } \frac { 1 } { i - 1 }$$

A) $- \frac { 259 } { 1296 }$
B) 26
C) $\frac { 107 } { 504 }$
D) $\frac { 533 } { 840 }$

Question 40

Find the indicated sum.
$$\sum _ { i = 1 } ^ { 4 } \left( - \frac { 1 } { 2 } \right) ^ { i }$$

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

Question 41

Find the common difference for the arithmetic sequence.
-12, -16, -20, -24, . . .

A) 12
B) -12
C) -4
D) -8

Question 42

Express the sum using summation notation. Use a lower limit of summation, not necessarily 1, and k for the index of summation.
$$15 + 19 + 23 + 27 + \ldots + 47$$

A) $\sum _ { k = 2 } ^ { 10 } 4 k + 7$
B) $\sum _ { k = 1 } ^ { 10 } 4 k + 7$
C) $\sum _ { k = 0 } ^ { 32 } 4 k + 7$
D) $\sum _ { k = 2 } ^ { 32 } 4 k + 7$

Question 43

Write the first five terms of the arithmetic sequence with the given first term, a1, and common difference, d.
$$a _ { 1 } = \frac { 7 } { 2 } , d = \frac { 5 } { 2 }$$

A) $\frac { 7 } { 2 } , 6 , \frac { 17 } { 2 } , 11 , \frac { 27 } { 2 }$
B) $\frac { 7 } { 2 } , 1 , - \frac { 3 } { 2 } , - 4 , - \frac { 13 } { 2 }$
C) $\frac { 7 } { 2 } , \frac { 1 } { 2 } , - \frac { 1 } { 2 } , - 1 , - \frac { 13 } { 10 }$
D) $\frac { 7 } { 2 } , 3 , \frac { 17 } { 6 } , \frac { 11 } { 4 } , \frac { 27 } { 10 }$

Question 44

Write the first five terms of the arithmetic sequence with the given first term, a1, and common difference, d.
a1 = 11; d = -2

A) 15, 12, 9, 6, 3
B) -11, -9, -7, -5, -3
C) 0, 11, 9, 7, 5
D) 11, 9, 7, 5, 3

Question 45

Write the first five terms of the arithmetic sequence with the given first term, a1, and common difference, d.
a1 = 9; d = 5

A) 9, 13, 17, 21, 25
B) 0, 9, 14, 19, 24
C) 14, 19, 24, 29, 34
D) 9, 14, 19, 24, 29

Question 46

Find the common difference for the arithmetic sequence.
6, 10, 14, 18, . . .

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

Question 47

Solve the problem.
The finite sequence whose general term is an = 0.13n2 - 1.09n + 7.03, where n = 1, 2, 3, . . ., 9 models the total operating costs, in millions of dollars, for a company for nine consecutive years. Find $\sum _ { \mathrm { i } = 1 } ^ { 4 } \mathrm { a } _ { \mathrm { i } }$

A) $\$ 24.28$ million
B) \$21.12 million
C) $\$ 30.35$ million
D) $\$ 25.95$ million

Question 48

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

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

Question 49

Write the first five terms of the arithmetic sequence with the given first term, a1, and common difference, d.
$$a _ { 1 } = - 0.4 , d = 0.7$$

A) $- 0.4 , - 1.1 , - 1.8 , - 2.5 , - 3.2$
B) $- 0.4,0.3,1,1.7,2.4$
C) $- 1.1 , - 1.8 , - 2.5 , - 3.2 , - 3.9$
D) $0.3,1,1.7,2.4,3.1$

Question 50

Express the sum using summation notation. Use a lower limit of summation, not necessarily 1, and k for the index of summation.
$$4 + \frac { 9 } { 2 } + 5 + \frac { 11 } { 2 } + \ldots + \frac { 17 } { 2 }$$

A) $\sum _ { k = 2 } ^ { 17 } \frac { k } { 2 }$
B) $\sum _ { k = 8 } ^ { 17 } \frac { k } { 2 }$
C) $\sum _ { k = 8 } ^ { 12 } \frac { k } { 2 }$
D) $\sum _ { k = 1 } ^ { 17 } \frac { \mathrm { k } } { 2 }$

Question 51

Solve the problem.
The bar graph below shows a company's yearly profits from 2003 to 2011. Let an represent the company's profit, in millions, in year n, where n = 1 corresponds to 2003, n = 2 corresponds to 2004, and so on.
Find $\sum _ { \mathrm { i } = 1 } ^ { 8 } \mathrm { a } _ { \mathrm { i } }$

A) $\$ 490.9$ million
B) $\$ 127.8$ million
C) \$544.6 million
D) $\$ 528.5$ million

Question 52

Write the first five terms of the arithmetic sequence with the given first term, a1, and common difference, d.
$$\mathrm { a } _ { 1 } = - 28 ; \mathrm { d } = 6$$

A) $- 16 , - 22 , - 28 , - 34 , - 40$
B) $- 28 , - 22 , - 16 , - 10 , - 4$
C) $- 4 , - 10 , - 16 , - 22 , - 28$
D) $- 16 , - 10 , - 4,2,8$

Question 53

Express the sum using summation notation. Use a lower limit of summation, not necessarily 1, and k for the index of summation.
$$8 + 9 + 10 + 11 + \ldots + 32$$

A) $\sum _ { k = 8 } ^ { 32 } ( k + 3 )$
B) $\sum _ { k = 1 } ^ { 24 } ( k + 3 )$
C) $\sum _ { k = 5 } ^ { 29 } ( k + 3 )$
D) $\sum _ { k = 11 } ^ { 35 } ( \mathrm { k } + 3 )$

Question 54

Find the common difference for the arithmetic sequence.
746, 737, 728, 719, . . .

A) 746
B) -9
C) 9
D) -746

Question 55

Find the common difference for the arithmetic sequence.
8, 13, 18, 23, . . .

A) 3.75
B) 15
C) 5
D) 8

Question 56

Express the sum using summation notation. Use 1 as the lower limit of summation and i for the index of summation.
$a + a r + a r ^ { 2 } + \ldots + a r ^ { 10 }$

A) $\sum _ { i = 1 } ^ { 10 } a r ^ { i }$
B) $\sum _ { \mathrm { i } = 1 } ^ { 10 } \left( \mathrm { ar } ^ { \mathrm { i } } - 1 \right.$
C) $\sum _ { i = 1 } ^ { 11 } a r ^ { i - 1 }$
D) $\sum _ { i = 1 } ^ { 10 } ( a r ) ^ { i }$

Question 57

Express the sum using summation notation. Use a lower limit of summation, not necessarily 1, and k for the index of summation.
$$1 ^ { 5 } + 2 ^ { 5 } + 3 ^ { 5 } + \ldots + 7 ^ { 5 }$$

A) $\sum _ { k = 0 } ^ { 7 } k ^ { 5 }$
B) $\sum _ { k = 1 } ^ { 7 } k ^ { 5 }$
C) $\sum _ { k = 2 } ^ { 7 } ( k - 1 ) ^ { 5 }$
D) $\sum _ { \mathrm { k } = 1 } ^ { \mathrm { i } } \mathrm { k } ^ { 5 }$

Question 58

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

Question 59

Express the sum using summation notation. Use a lower limit of summation, not necessarily 1, and k for the index of summation.
$$a + a r + a r ^ { 2 } + \ldots + a r ^ { 15 }$$

A) $\sum _ { \mathrm { k } = 1 } ^ { 15 } a r ^ { \mathrm { k } }$
B) $\sum _ { k = 0 } ^ { 15 } a r ^ { k }$
C) $\sum _ { \mathrm { k } = 1 } ^ { 16 } a \mathrm { r } ^ { \mathrm { k } }$
D) $\sum _ { k = 0 } ^ { 15 } ( a r ) ^ { k }$

Question 60

Write the first five terms of the arithmetic sequence with the given first term, a1, and common difference, d.
a1 = 14; d = -4

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

Question 61

Write out the first three terms and the last term of the arithmetic sequence.
$$\sum _ { i = 1 } ^ { 70 } - 2 i$$

A) $- 2 + 4 - 12 + \ldots - 280$
B) $- 1 - 2 - 4 - \ldots - 140$
C) $- 2 - 4 - 8 - \ldots - 280$
D) $- 2 - 4 - 6 - \ldots - 140$

Question 62

Solve the problem.
The population of a town is increasing by 300 inhabitants each year. If its current population is 20,506 and this trend continues, what would its population be in 8 years?

A) 22,606 inhabitants
B) 163,964 inhabitants
C) 22,906 inhabitants
D) 327,928 inhabitants

Question 63

Use the partial sum formula to find the partial sum of the given arithmetic sequence.
Find the sum of the first eight terms of the arithmetic sequence: 3, 5, 7, . . . .

A) 160
B) 40
C) 15
D) 80

Question 64

Write out the first three terms and the last term of the arithmetic sequence.
$$\sum _ { i = 1 } ^ { 12 }$$

A) $- 5 + 0 + 5 + \ldots + 55$
B) $0 + 5 + 10 + \ldots + 55$
C) $0 + 20 + 70 + \ldots + 295$
D) $- 5 - 0 + 5 - \ldots + 55$

Question 65

Use the partial sum formula to find the partial sum of the given arithmetic sequence.
Find the sum of the first 25 terms of the arithmetic sequence: -5, 2, 9, 16, . . . .

A) 1896
B) 1650
C) 2063
D) 1975

Question 66

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 a14 when a1 = 23, d = -3.

A) -39
B) -19
C) 62
D) -16

Question 67

Solve the problem.
To train for a race, Will begins by jogging 11 minutes one day per week. He increases his jogging time by 6 minutes each week. Write the general term of this arithmetic sequence, and find how many weeks it takes for him to reach a jogging time of one hour. A) $a _ { n } = 6 n + 11 ; 9$ weeks
B) $a _ { n } = 6 n + 5 ; 9$ weeks
C) $a _ { n } = 6 n + 5 ; 10$ weeks
D) $a _ { n } = 6 n + 11 ; 10$ weeks

Question 68

Use the partial sum formula to find the partial sum of the given arithmetic sequence.
Find the sum of the odd integers between 22 and 52.

A) 592
B) 555
C) 518
D) 629

Question 69

Use the formula for the sum of the first n terms of an arithmetic sequence to find the indicated sum.
$$\sum _ { i = 1 } ^ { 26 } ( - 3 i + 8 )$$

A) $- 845$
В) $- 715$
C) $- 806$
D) $- 624$

Question 70

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 37 when $a _ { 1 } = 5 , d = \frac { 2 } { 3 }$ .

A) $- \frac { 59 } { 3 }$
B) $- 19$
C) 29
D) $\frac { 89 } { 3 }$

Question 71

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 32 when a1 = 3 , d = -4 .

A) -125
B) 131
C) -121
D) 127

Question 72

Use the formula for the sum of the first n terms of an arithmetic sequence to find the indicated sum.
$$\sum _ { \mathrm { i } = 1 } ^ { 49 } ( 5 \mathrm { i } + 5 )$$

A) $6247.5$
B) $6541.5$
C) 6713
D) 6370

Question 73

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 a1 = -9 , d = 4 .

A) -41
B) -37
C) 23
D) 19

Question 74

Use the partial sum formula to find the partial sum of the given arithmetic sequence.
Find 2 + 4 + 6 + 8 + . . ., the sum of the first 40 positive even integers.

A) 1644
B) 1599
C) 1640
D) 1595

Question 75

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.
$$a _ { 1 } = - \frac { 3 } { 5 } , d = \frac { 4 } { 5 }$$

A) $a _ { n } = \frac { 4 } { 5 } n - \frac { 7 } { 5 } ; a _ { 20 } = \frac { 73 } { 5 }$
B) $a _ { n } = - \frac { 3 } { 5 } n + \frac { 7 } { 5 } ; a _ { 20 } = - \frac { 53 } { 5 }$
C) $a _ { n } = \frac { 4 } { 5 } n - \frac { 3 } { 5 } ; a _ { 20 } = \frac { 77 } { 5 }$
D) $a _ { n } = - \frac { 3 } { 5 } n + \frac { 4 } { 5 } ; a _ { 20 } = - \frac { 56 } { 5 }$

Question 76

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.
$$a _ { 1 } = - 9 , d = - 0.5$$

A) $a _ { n } = - 9 n + 8.5 ; a _ { 20 } = - 171.5$
B) $a _ { n } = - 0.5 n - 9 ; a _ { 20 } = - 19$
C) $a _ { n } = - 0.5 n - 8.5 ; a _ { 20 } = - 18.5$
D) $a _ { n } = - 9 n - 0.5 ; a _ { 20 } = - 180.5$

Question 77

Use the partial sum formula to find the partial sum of the given arithmetic sequence.
Find the sum of the first five terms of the arithmetic sequence: -10, -14, -18, . . . .

A) -70
B) 90
C) - 90
D) -42

Question 78

Use the formula for the sum of the first n terms of an arithmetic sequence to find the indicated sum.
$$\sum _ { i = 1 } ^ { 27 } ( 6 i - 1 )$$

A) $2362.5$
B) 2457
C) 2241
D) 2160

Question 79

Solve the problem.
Jacie is considering a job that offers a monthly starting salary of $3500 and guarantees her a monthly raise of $110 during her first year on the job. Find the general term of this arithmetic sequence and her monthly salary at the end of her first year. A) $a _ { n } = 3390 + 110 n$ ; $\$ 4710$
B) $a _ { n } = 3500 + 110 n ; \$ 4820$
C) $a _ { n } = 3500 + 110 n ; \$ 4710$
D) $a _ { n } = 3390 + 110 ( n - 1 ) ; \$ 4600$

Question 80

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 a50 when a1 = -9, d = 3.

A) -159
B) 141
C) 138
D) -156