Deck 10: Radicals, Radical Functions, and Rational Exponents

Question 1

Write the first four terms of the sequence whose general term is given.
$$a _ { n } = \left( - \frac { 2 } { 5 } \right) ^ { n }$$

A) $\frac { 2 } { 5 } , - \frac { 2 } { 10 } , \frac { 2 } { 15 } , - \frac { 2 } { 20 }$
B) $- \frac { 2 } { 5 } , - \frac { 4 } { 25 } , - \frac { 8 } { 125 } , - \frac { 16 } { 625 }$
C) $- \frac { 2 } { 5 } , \frac { 2 } { 10 } , - \frac { 2 } { 15 } , - \frac { 2 } { 20 }$
D) $- \frac { 2 } { 5 } , \frac { 4 } { 25 } , - \frac { 8 } { 125 } , \frac { 16 } { 625 }$

Answer 1

$- \frac { 2 } { 5 } , \frac { 4 } { 25 } , - \frac { 8 } { 125 } , \frac { 16 } { 625 }$

Question 2

Write the first four terms of the sequence whose general term is given.
$$a _ { n } = 4 ( 2 n - 3 )$$

A) $- 12 , - 4,4,12,20$
B) $- 1,1,3,5,7$
C) $- 4,4,12,20,28$
D) $- 4 , - 8 , - 12 , - 16 , - 20$

Answer 2

$- 4,4,12,20,28$

Question 3

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

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

Answer 3

$2,4,8,16$

Question 4

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

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

Question 5

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

A) $- 5 , - 6 , - 7 , - 8$
B) $5,6,7,8$
C) $- 5,6 , - 7,8$
D) $- 5 , - 12 , - 21 , - 32$

Question 6

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

A) $\frac { 1 } { 3 } , \frac { 3 } { 11 } , \frac { 2 } { 9 } , \frac { 5 } { 27 }$
B) $\frac { 1 } { 3 } , \frac { 1 } { 3 } , \frac { 3 } { 8 } , \frac { 2 } { 5 }$
C) $\frac { 1 } { 2 } , \frac { 1 } { 3 } , \frac { 3 } { 8 } , \frac { 2 } { 5 }$
D) $\frac { 1 } { 3 } , \frac { 1 } { 3 } , \frac { 3 } { 11 } , \frac { 2 } { 9 }$

Question 7

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

A) $5,10,15,20$
B) $4,3,2,1$
C) $0,5,10,15$
D) $6,7,8,9$

Question 8

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

A) $- 12,96 , - 720,5760$
B) $- 4 , - 24 , - 144 , - 960$
C) $- 12 , - 48 , - 240 , - 1440$
D) $- 4,12 , - 48,240$

Question 9

Solve the problem.
A deposit of $7000 is made in an account that earns 7.2% interest compounded quarterly. The balance in the account after n quarters is given by the sequence $$a _ { n } = 7000 \left( 1 + \frac { 0.072 } { 4 } \right) ^ { n } , n = 1,2,3 , \ldots$$ Find the balance in the account after four years by computing a16

A) $4087.38
B) $5321.38
C) $9312.42
D) $7517.77

Question 10

Write the first four terms of the sequence whose general term is given.
$$a _ { n } = n - 6$$

A) $- 5 , - 4 , - 3 , - 2$
B) $1,2,3,4$
C) $- 6 , - 5 , - 4 , - 3$
D) $- 24 , - 18 , - 12 , - 6$

Question 11

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

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

Question 12

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

A) $4 , - 16 , - 64 , - 256$
B) $4 , - 16,64 , - 256$
C) $- 4,16 , - 64,256$
D) $- 4 , - 16 , - 64 , - 256$

Question 13

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

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

Question 14

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 15

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

A) $\frac { 3 } { 0 } , \frac { 6 } { 0 } , \frac { 9 } { 2 } , 2$
B) $1,8 , \frac { 27 } { 2 } , \frac { 32 } { 3 }$
C) $\frac { 1 } { 0 } , \frac { 8 } { 0 } , \frac { 27 } { 2 } , \frac { 32 } { 3 }$
D) $3,6 , \frac { 9 } { 2 } , 2$

Question 16

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

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

Question 17

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

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

Question 18

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

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

Question 19

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

A) $8 , - 9,10 , - 11$
B) $8 , - 18,30 , - 44$
C) $- 8,9 , - 10,11$
D) $- 9,10 , - 11,12$

Question 20

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

A) $- 3 , - 7 , - 11 , - 15$
B) $3,7,11,15$
C) $5,9,13,17$
D) $3,4,5,6$

Question 21

Find the indicated sum.
$$\sum _ { i = 3 } ^ { 6 } ( 4 i - 4 )$$

A) 32
B) 60
C) 56
D) 48

Question 22

Express the sum using summation notation. Use 1 as the lower limit of summation and i for the index of summation.
$$\frac { 1 } { 3 } + \frac { 1 } { 2 } + \frac { 3 } { 5 } + \ldots + \frac { 13 } { 15 }$$

A) $\sum _ { i = 1 } ^ { 13 } \frac { i } { i + 2 }$
B) $\sum _ { i = 0 } ^ { 13 } \frac { i } { i + 2 }$
C) $\sum _ { i = 2 } ^ { 13 } \frac { i } { i + 1 }$
D) $\sum _ { \mathrm { i } = 1 } ^ { \mathrm { n } } \frac { \mathrm { i } } { \mathrm { i } + 2 }$

Question 23

Find the indicated sum.
$$\sum _ { i = 9 } ^ { 12 } \frac { 1 } { i + 3 }$$

A) $- \frac { 323 } { 660 }$
B) $\frac { 820 } { 2187 }$
C) 54
D) $\frac { 543 } { 1820 }$

Question 24

Express the sum using summation notation. Use 1 as the lower limit of summation and i for the index of summation.
$$3 + 6 + 9 + \ldots + 21$$

A) $\sum _ { i = 1 } ^ { 7 } 3 i ^ { 2 }$
B) $\sum _ { i = 1 } ^ { 7 } i ^ { 2 }$
C) $\sum _ { i = 1 } ^ { 7 } 3 i$
D) $\sum _ { i = 0 } ^ { 7 } 3 i$

Question 25

Find the indicated sum.
$\sum _ { i = 3 } ^ { 5 } \left( i ^ { 2 } + 8 \right)$

A) 48
B) 36
C) 74
D) 95

Question 26

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

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

Question 27

Find the indicated sum.
$$\sum _ { i = 4 } ^ { 7 } 2 i$$

A) 14
B) 22
C) 44
D) 30

Question 28

Find the indicated sum.
$\sum _ { k = 2 } ^ { 4 } k ( k + 3 )$

A) 56
B) 38
C) 60
D) 27

Question 29

Find the indicated sum.
$\sum _ { i = 4 } ^ { 10 } 12$

A) 72
B) 84
C) 540
D) 588

Question 30

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

A) $\frac { 20 } { 81 }$
B) $- \frac { 16 } { 81 }$
C) $- \frac { 20 } { 81 }$
D) $\frac { 40 } { 81 }$

Question 31

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

A) $\frac { 11 } { 24 }$
B) $\frac { 5 } { 16 }$
C) $\frac { 1 } { 16 }$
D) $\frac { 25 } { 48 }$

Question 32

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

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

Question 33

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

A) -14
B) 6
C) 2
D) 14

Question 34

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

Question 35

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

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

Question 36

Find the indicated sum.
$$\sum _ { i = 1 } ^ { 5 } ( i - 7 )$$

A) $- 8$
B) $- 20$
C) $- 18$
D) $- 2$

Question 37

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

Question 38

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

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

Question 39

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

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

Question 40

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

A) $\sum _ { i = 0 } ^ { n } \frac { a + i } { i }$
B) $\sum _ { i = 0 } ^ { 5 } \frac { a + i } { i }$
C) $\sum _ { i = 1 } ^ { 5 } \frac { a + i } { i }$
D) $\sum _ { i = 1 } ^ { n } \frac { a + i } { i }$

Question 41

Express the sum using summation notation. Use a lower limit of summation, not necessarily 1, and k for the index of
summation.
$$a + a r + a r ^ { 2 } + \ldots + a r ^ { 13 }$$

A) $\sum _ { \mathrm { k } = 1 } ^ { 14 } a r ^ { \mathrm { k } }$
B) $\sum _ { k = 0 } ^ { 13 } ( a r ) ^ { k }$
C) $\sum _ { k = 0 } ^ { 13 } a r ^ { k }$
D) $\sum _ { k = 1 } ^ { 13 } a r ^ { k }$

Question 42

Write the first five terms of the arithmetic sequence with the given first term, a1, and common difference, d.
a1 = -1.7, d = -1.5

A) -1.7, -3.2, -4.7, -6.2, -7.7
B) -1.7, -0.2, 1.3, 2.8, 4.3
C) -0.2, 1.3, 2.8, 4.3, 5.8
D) -3.2, -4.7, -6.2, -7.7, -9.2

Question 43

Write the first five terms of the arithmetic sequence with the given first term, a1, and common difference, d.
a1 = 5; d = -1

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

Question 44

Express the sum using summation notation. Use a lower limit of summation, not necessarily 1, and k for the index of
summation.
$$\frac { 6 } { 7 } + \frac { 7 } { 8 } + \frac { 8 } { 9 } + \frac { 9 } { 10 } + \ldots + \frac { 19 } { 20 }$$

A) $\sum _ { k = 7 } ^ { 19 } \frac { k } { k + 1 }$
B) $\sum _ { k = 7 } ^ { 19 } \frac { k + 1 } { k }$
C) $\sum _ { k = 6 } ^ { 19 } \frac { k } { k + 1 }$
D) $\sum _ { \mathrm { k } = 6 } ^ { 19 } \frac { \mathrm { k } + 1 } { \mathrm { k } }$

Question 45

Find the common difference for the arithmetic sequence.
583, 588, 593, 598, . . .

A) 583
B) 5
C) -583
D) -5

Question 46

Express the sum using summation notation. Use a lower limit of summation, not necessarily 1, and k for the index of
summation.
$$5 + 6 + 7 + 8 + \ldots + 34$$

A) $\sum _ { k = 1 } ^ { 29 } ( k - 1 )$
B) $\sum _ { k = 4 } ^ { 33 } ( k - 1 )$
C) $\sum _ { k = 5 } ^ { 34 } ( k - 1 )$
D) $\sum _ { k = 6 } ^ { 35 } ( k - 1 )$

Question 47

Solve the problem.
The finite sequence whose general term is $\mathrm { a } _ { \mathrm { n } } = 0.14 \mathrm { n } ^ { 2 } - 1.06 \mathrm { n } + 7.45$ , where $\mathrm { n } = 1,2,3 , \ldots , 9$ 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) $23.4 million
B) $32.65 million
C) $29.05 million
D) $26.12 million

Question 48

Write the first five terms of the arithmetic sequence with the given first term, a1, and common difference, d.
$$a _ { 1 } = \frac { 3 } { 4 } , d = \frac { 5 } { 4 }$$

A) $\frac { 3 } { 4 } , - \frac { 1 } { 2 } , - \frac { 7 } { 4 } , - 3 , - \frac { 17 } { 4 }$
B) $\frac { 3 } { 4 } , 2 , \frac { 13 } { 4 } , \frac { 9 } { 2 } , \frac { 23 } { 4 }$
C) $\frac { 3 } { 4 } , 1 , \frac { 13 } { 12 } , \frac { 9 } { 8 } , \frac { 23 } { 20 }$
D) $\frac { 3 } { 4 } , - \frac { 1 } { 4 } , - \frac { 7 } { 12 } , - \frac { 3 } { 4 } , - \frac { 17 } { 20 }$

Question 49

Write the first five terms of the arithmetic sequence with the given first term, a1, and common difference, d.
a1 = 1; d = 2

A) 3, 5, 7, 9, 11
B) 0, 1, 3, 5, 7
C) 1, 2, 3, 4, 5
D) 1, 3, 5, 7, 9

Question 50

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

Question 51

Find the common difference for the arithmetic sequence.
2, -1, -4, -7, . . .

A) 9
B) -3
C) -9
D) -6

Question 52

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.
$$\text { Find } \sum _ { i = 4 } ^ { 9 } a _ { i }$$

A) $505.8 million
B) $549.6 million
C) $167.9 million
D) $491.7 million

Question 53

Write the first five terms of the arithmetic sequence with the given first term, a1, and common difference, d.
a1 = 18; d = -4

A) 0, 18, 14, 10, 6
B) 22, 17, 12, 7, 2
C) 18, 14, 10, 6, 2
D) -18, -14, -10, -6, -2

Question 54

Write the first five terms of the arithmetic sequence with the given first term, a1, and common difference, d.
a1 = -36; d = 9

A) 0, -9, -18, -27, -36
B) -18, -9, 0, 9, 18
C) -18, -27, -36, -45, -54
D) -36, -27, -18, -9, 0

Question 55

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

Question 56

Find the common difference for the arithmetic sequence.
3, 5, 7, 9, . . .

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

Question 57

Express the sum using summation notation. Use a lower limit of summation, not necessarily 1, and k for the index of
summation.
$$3 + \frac { 7 } { 2 } + 4 + \frac { 9 } { 2 } + \ldots + \frac { 15 } { 2 }$$

A) $\sum _ { k = 2 } ^ { 15 } \frac { k } { 2 }$
B) $\sum _ { k = 6 } ^ { 10 } \frac { k } { 2 }$
C) $\sum _ { k = 1 } ^ { 15 } \frac { k } { 2 }$
D) $\sum _ { k = 6 } ^ { 15 } \frac { k } { 2 }$

Question 58

Express the sum using summation notation. Use a lower limit of summation, not necessarily 1, and k for the index of
summation.
$$1 ^ { 3 } + 2 ^ { 3 } + 3 ^ { 3 } + \ldots + 8 ^ { 3 }$$

A) $\sum _ { k = 1 } ^ { i } k ^ { 3 }$
B) $\sum _ { k = 2 } ^ { 8 } ( k - 1 ) ^ { 3 }$
C) $\sum _ { k = 0 } ^ { 8 } k ^ { 3 }$
D) $\sum _ { k = 1 } ^ { 8 } k ^ { 3 }$

Question 59

Find the common difference for the arithmetic sequence.
7, 9, 11, 13, . . .

A) 6
B) 2
C) 1.5
D) 7

Question 60

Express the sum using summation notation. Use 1 as the lower limit of summation and i for the index of summation.
$$a + a r + a r ^ { 2 } + \ldots + a r ^ { 14 }$$

A) $\sum _ { \mathrm { i } = 1 } ^ { 14 } a r ^ { \mathrm { i } }$
B) $\sum _ { \mathrm { i } = 1 } ^ { 14 } ( \mathrm { ar } ) ^ { \mathrm { i } }$
C) $\sum _ { i = 1 } ^ { 15 } a r ^ { i-1 }$
D) $\sum _ { \mathrm { i } = 1 } ^ { 14 } ( \mathrm { ar } ) ^ { \mathrm { i } - 1 }$

Question 61

Write out the first three terms and the last term of the arithmetic sequence.
$$\sum _ { i = 1 } ^ { 60 } - 5 i$$

A) $- 1 - 5 - 10 - \ldots - 300$
B) $- 5 - 25 - 125 - \ldots - 1500$
C) $- 5 + 25 - 75 + \ldots - 1500$
D) $- 5 - 10 - 15 - \ldots - 300$

Question 62

Write a formula for the general term (the nth term) of the arithmetic sequence. Then use the formula for an to find a20,
the 20th term of the sequence.
2 , 6 , 10 , 14 , 18 , . . .

A) $a _ { n } = 2 n - 4 ; a _ { 20 } = 36$
B) $a _ { n } = 4 n + 2 ; a _ { 20 } = 82$
C) $a _ { n } = 4 n - 2 ; a _ { 20 } = 78$
D) $a _ { n } = n + 4 ; a _ { 20 } = 24$

Question 63

Use the partial sum formula to find the partial sum of the given arithmetic sequence.
Find 1 + 3 + 5 + 7 + . . ., the sum of the first 55 positive odd integers.

A) 2970
B) 3025
C) 3029
D) 2966

Question 64

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 17 when a1 = -4 , d = - 1 .

A) 12
B) 13
C) - 20
D) - 21

Question 65

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 a90 when a1 = -14, d = -5.

A) -464
B) 431
C) -459
D) 436

Question 66

Write a formula for the general term (the nth term) of the arithmetic sequence. Then use the formula for an to find a20,
the 20th term of the sequence.
$$a _ { 1 } = - \frac { 3 } { 4 } , d = \frac { 5 } { 4 }$$

A) $a _ { n } = \frac { 5 } { 4 } n - 2 ; a _ { 20 } = 23$
B) $a _ { n } = \frac { 5 } { 4 } n - \frac { 3 } { 4 } ; a _ { 20 } = \frac { 97 } { 4 }$
C) $a _ { n } = - \frac { 3 } { 4 } n + \frac { 5 } { 4 } ; a _ { 20 } = - \frac { 55 } { 4 }$
D) $a _ { n } = - \frac { 3 } { 4 } n + 2 ; a _ { 20 } = - 13$

Question 67

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 a11 when a1 = 20, d = -6.

A) 80
B) -46
C) -40
D) -60

Question 68

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: 10, 15, 20, . . . .

A) 220
B) 45
C) 120
D) 440

Question 69

Write a formula for the general term (the nth term) of the arithmetic sequence. Then use the formula for an to find a20,
the 20th term of the sequence.
-21, -26 , -31, -36, . . .

A) $a _ { n } = 5 n + 16 ; a _ { 20 } = 116$
B) $a _ { n } = 5 n + 21 ; a _ { 20 } = 121$
C) $a _ { n } = - 5 n - 16 ; a _ { 20 } = - 116$
D) $a _ { n } = - 5 n - 21 ; a _ { 20 } = - 121$

Question 70

Use the partial sum formula to find the partial sum of the given arithmetic sequence.
Find the sum of the first four terms of the arithmetic sequence: -3, -15, -27, . . . .

A) 84
B) -60
C) - 84
D) -45

Question 71

Write a formula for the general term (the nth term) of the arithmetic sequence. Then use the formula for an to find a20,
the 20th term of the sequence.
27, 18 , 9, 0, . . .

A) $a _ { n } = 27 - 9 n ; a _ { 20 } = - 153$
B) $a _ { n } = 36 - 9 n ; a _ { 20 } = - 144$
C) $a _ { n } = 9 n - 27 ; a _ { 20 } = 153$
D) $a _ { n } = 9 n - 36 ; a _ { 20 } = 144$

Question 72

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 = 3 .

A) 93
B) -96
C) -99
D) 90

Question 73

Solve the problem.
To train for a race, Will begins by jogging 11 minutes one day per week. He increases his jogging time by 3 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) $a _ { n } = 3 n + 11 ; 18$ weeks
B) $a _ { n } = 3 n + 11 ; 17$ weeks
C) $a _ { n } = 3 n + 8 ; 18$ weeks
D) $a _ { n } = 3 n + 8 ; 17$ weeks

Question 74

Use the partial sum formula to find the partial sum of the given arithmetic sequence.
Find the sum of the first 70 terms of the arithmetic sequence: 1, 8, 15, 22, . . . .

A) 16,733
B) 15,990
C) 17,220
D) 16,975

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.
Find a8 when a1 = -8 , d = -5 .

A) -43
B) 27
C) -48
D) 32

Question 76

Solve the problem.
Jacie is considering a job that offers a monthly starting salary of $3000 and guarantees her a monthly raise of $130 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) $a _ { n } = 2870 + 130 n ; \$ 4430$
B) $a _ { n } = 3000 + 130 n ; \$ 4560$
C) $a _ { n } = 3000 + 130 n ; \$ 4430$
D) $a _ { n } = 2870 + 130 ( n - 1 ) ; \$ 4300$

Question 77

Solve the problem.
The population of a town is increasing by 400 inhabitants each year. If its current population is 29,089 and this trend continues, what would its population be in 8 years?

A) 232,600 inhabitants
B) 32,289 inhabitants
C) 465,200 inhabitants
D) 31,889 inhabitants

Question 78

Write a formula for the general term (the nth term) of the arithmetic sequence. Then use the formula for an to find a20,
the 20th term of the sequence.
$$a _ { 1 } = - 7 , d = 0.5$$

A) $a _ { n } = - 7 n + 7.5 ; a _ { 20 } = - 132.5$
B) $a _ { n } = - 7 n + 0.5 ; a _ { 20 } = - 139.5$
C) $a _ { n } = 0.5 n - 7 ; a _ { 20 } = 3$
D) $a _ { n } = 0.5 n - 7.5 ; a _ { 20 } = 2.5$

Question 79

Use the partial sum formula to find the partial sum of the given arithmetic sequence.
Find the sum of the odd integers between 24 and 66.

A) 900
B) 990
C) 945
D) 1035

Question 80

Write a formula for the general term (the nth term) of the arithmetic sequence. Then use the formula for an to find a20,
the 20th term of the sequence.
3 , 12 , 21 , 30 , 39 , . . .

A) $a _ { n } = 6 n - 2 ; a _ { 20 } = 118$
B) $a _ { n } = 9 n - 2 ; a _ { 20 } = 178$
C) $a _ { n } = 6 n - 9 ; a _ { 20 } = 111$
D) $a _ { n } = 9 n - 6 ; a _ { 20 } = 174$