Deck 9: Sequences and Series; Counting and Probability

Question 1

Write the first four terms of the recursive sequence.
-3, 9, -27, 81, . . . A) $a _ { n } = - 3 + ( - 3 ) ^ { n }$
B) $a _ { n } = - 9 ^{n - 1}$
C) $a _ { n } = - 3 ( - 3 ) ^ { n - 1 }$
D) $a _ { n } = - 3 ( - 3 ) ^ { n }$

Answer 1

C

Question 2

Write the first four terms of the sequence.
$$a _ { n } = \frac { 6 n - 1 } { n ^ { 2 } + 6 n }$$

A) $\frac { 5 } { 7 } , \frac { 11 } { 10 } , \frac { 17 } { 15 } , \frac { 23 } { 22 }$
B) $\frac { 5 } { 6 } , \frac { 11 } { 12 } , \frac { 17 } { 18 } , \frac { 23 } { 24 }$
C) $1 , \frac { 13 } { 16 } , \frac { 19 } { 27 } , \frac { 5 } { 8 }$
D) $\frac { 5 } { 7 } , \frac { 11 } { 16 } , \frac { 17 } { 27 } , \frac { 23 } { 40 }$

Answer 2

D

Question 3

Write the first four terms of the recursive sequence.
2 , 10 , 18 , 26 , 34 , . . . A) $a _ { n } = 2 ( 8 ) ^ { n - 1 }$
B) $a _ { n } = 8 n - 3$
C) $a _ { n } = 8 n - 6$
D) $a _ { n } = 6 n - 8$

Answer 3

C

Question 4

Perform the indicated operations and simplify the result. Leave the answer in factored form.
$a _ { 1 } = 2 , a _ { n } = n - a _ { n } - 1$ for $n \geq 2$

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

Question 5

Write the first four terms of the sequence.
$$a _ { n } = \frac { n ^ { 5 } } { ( n + 1 ) ! }$$

A) $\frac { 5 } { 2 } , \frac { 5 } { 3 } , \frac { 5 } { 4 } , 1$
B) $\frac { 1 } { 2 } , \frac { 16 } { 3 } , \frac { 81 } { 8 } , \frac { 128 } { 15 }$
C) $\frac { 5 } { 2 } , \frac { 5 } { 3 } , \frac { 5 } { 8 } , \frac { 1 } { 6 }$
D) $\frac { 1 } { 2 } , \frac { 16 } { 3 } , \frac { 81 } { 4 } , \frac { 256 } { 5 }$

Question 6

Perform the indicated operations and simplify the result. Leave the answer in factored form.
$a _ { 1 } = - 2 , a _ { n } = a _ { n } - 1 + 6$ for $n \geq 2$

A) $0,6,12,18$
B) $- 2,6,12,18$
C) $- 2,4,10,16$
D) $4,10,16,22$

Question 7

Write the first four terms of the sequence.
$$a _ { n } = \frac { 2 ^ { n } } { ( n + 2 ) ! }$$

A) $\frac { 1 } { 3 } , \frac { 1 } { 6 } , \frac { 2 } { 15 } , \frac { 2 } { 45 }$
B) $\frac { 2 } { 3 } , 1 , \frac { 8 } { 5 } , \frac { 8 } { 3 }$
C) $\frac { 3 } { 2 } , 1 , \frac { 8 } { 5 } , \frac { 3 } { 8 }$
D) $\frac { 1 } { 3 } , \frac { 1 } { 6 } , \frac { 1 } { 15 } , \frac { 1 } { 45 }$

Question 8

Perform the indicated operations and simplify the result. Leave the answer in factored form.
$$\mathrm { a } _ { \mathrm { n } } = \frac { ( - 1 ) ^ { n } } { ( \mathrm { n } + 1 ) ( \mathrm { n } + 4 ) }$$

A) $- \frac { 1 } { 10 } , \frac { 1 } { 18 } , - \frac { 1 } { 28 } , \frac { 1 } { 40 }$
B) $\frac { 1 } { 7 } , - \frac { 1 } { 9 } , \frac { 1 } { 11 } , - \frac { 1 } { 13 }$
C) $\frac { 1 } { 10 } , - \frac { 1 } { 18 } , \frac { 1 } { 28 } , - \frac { 1 } { 40 }$
D) $- \frac { 1 } { 7 } , \frac { 1 } { 9 } , - \frac { 1 } { 11 } , \frac { 1 } { 13 }$

Question 9

Write the first four terms of the sequence.
$$a _ { n } = ( - 3 ) ^ { n }$$

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

Question 10

Write the first four terms of the recursive sequence.
-4, 16, -64, 256, -1024, . . . A) $a _ { n } = ( - 1 ) ^ { n } ( 4 ) ^ { n }$
B) $a _ { n } = ( - 1 ) ^ { n - 1 } ( 4 ) ^ { n }$
C) $a _ { n } = - 4 + 12 ( n - 1 )$
D) $a _ { n } = ( - 1 ) ^ { n } ( 4 n )$

Question 11

Write the first four terms of the sequence.
$$a _ { n } = 4 n - 1$$

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

Question 12

Write the first four terms of the sequence.
$$a _ { n } = 4 ^ { n }$$

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

Question 13

Write the first four terms of the sequence.
$$\mathrm { a } _ { \mathrm { n } } = 4 ( \mathrm { n } + 2 ) !$$

A) $8,48,288,1920$
B) $8,24,96,480$
C) $24,192,1440,11,520$
D) $24,96,480,2880$

Question 14

Perform the indicated operations and simplify the result. Leave the answer in factored form.
$a _ { 1 } = 2 , a _ { n } = \frac { a _ { n } - 1 } { n + 1 }$ for $n \geq 2$

A) $2 , \frac { 2 } { 3 } , \frac { 1 } { 6 } , \frac { 1 } { 30 }$
B) $2,2,1 , \frac { 1 } { 3 }$
C) $2,2 , \frac { 2 } { 3 } , \frac { 1 } { 6 }$
D) $2,1 , \frac { 1 } { 3 } , \frac { 1 } { 12 }$

Question 15

Write the first four terms of the recursive sequence.
$\frac { 2 } { 3 } , \frac { 3 } { 4 } , \frac { 4 } { 5 } , \frac { 5 } { 6 } , \frac { 6 } { 7 } , \ldots$

A) $a _ { n } = \frac { 2 } { n + 1 }$
B) $a _ { n } = \frac { n + 1 } { n + 2 }$
C) $a _ { n } = \frac { n } { n + 1 }$
D) $a _ { n } = \frac { 1 } { n + 2 }$

Question 16

Perform the indicated operations and simplify the result. Leave the answer in factored form.
$a _ { 1 } = 3 , a _ { n } = 3 a _ { n } - 1 - 5$ for $n \geq 2$

A) $3,14,47,146$
B) $3,4,22,76$
C) $3,9,27,81$
D) $3,4,7,16$

Question 17

Write the first four terms of the recursive sequence.
$a _ { 1 } = 8 , a _ { n } = 1 - \frac { 1 } { a _ { n - 1 } }$ for $n \geq 2$

A) $8 , \frac { 7 } { 8 } , - \frac { 1 } { 7 } , - 8$
B) $8 , \frac { 7 } { 8 } , - \frac { 1 } { 7 } , 8$
C) $8 , \frac { 7 } { 8 } , \frac { 1 } { 7 } , - 6$
D) $8 , - \frac { 7 } { 8 } , \frac { 15 } { 7 } , \frac { 8 } { 15 }$

Question 18

Write the first four terms of the recursive sequence.
1 ·5, 2 ·6, 3 ·7, 4 ·8, 5 ·9, . . . A) $a _ { n } = n ( n - 4 )$
B) $a _ { n } = n + 4 n$
C) $a _ { n } = n ( n + 4 )$
D) $a _ { n } = n ( n + 5 )$

Question 19

Write the first four terms of the sequence.
$$a _ { n } = \frac { 3 n + 1 } { 3 n }$$

A) $\frac { 7 } { 3 } , \frac { 10 } { 3 } , \frac { 13 } { 3 } , \frac { 16 } { 3 }$
B) $\frac { 4 } { 3 } , \frac { 7 } { 3 } , \frac { 10 } { 7 } , \frac { 13 } { 3 }$
C) $\frac { 4 } { 3 } , \frac { 7 } { 6 } , \frac { 10 } { 9 } , \frac { 13 } { 12 }$
D) $\frac { 7 } { 6 } , \frac { 10 } { 9 } , \frac { 13 } { 12 } , \frac { 16 } { 15 }$

Question 20

Write the first four terms of the sequence.
$$\mathrm { a } _ { \mathrm { n } } = ( - 1 ) ^ { \mathrm { n } - 1 } ( 8 \mathrm { n } - 5 )$$

A) $- 3,11 , - 19 , - 27$
B) $3 , - 21,19 , - 27$
C) $3 , - 11,19 , - 27$
D) $3,11,19,27$

Question 21

Find the indicated term of the sequence.
$$- 32,64 , - 128,256 , \ldots ; S _ { 5 }$$

A)672
B)-512
C)- 480
D)- 352

Question 22

Find the indicated term of the sequence.
-3, 9, -27, 81, . . .; a7

A)-567
B)2188
C)-6561
D)-2187

Question 23

The general term of a sequence is given. Find the indicated partial sum.
$$\sum _ { k = 2 } ^ { 4 } k ( k + 2 )$$

A) 24
B) 47
C) 32
D) 50

Question 24

The first several terms of a sequence are given. Find the indicated partial sum.
$$a _ { n } = 5 n - 2 ; S _ { 5 }$$

A)65
B)85
C)100
D)55

Question 25

The general term of a sequence is given. Find the indicated partial sum.
$$\sum _ { k = 2 } ^ { 5 } ( 4 k - 2 )$$

A) 48
B) 36
C) 26
D) 42

Question 26

Find the indicated term of the sequence.
$$- \frac { 1 } { 2 } , \frac { 1 } { 4 } , - \frac { 1 } { 8 } , \frac { 1 } { 16 } , \ldots ; S _ { 5 }$$

A) $- \frac { 15 } { 64 }$
B) $- \frac { 21 } { 64 }$
C) $- \frac { 11 } { 32 }$
D) $- \frac { 1 } { 32 }$

Question 27

The general term of a sequence is given. Find the indicated partial sum.
$$\sum _ { i = 2 } ^ { 5 } 9 i$$

A) 45
B) 81
C) 63
D) 126

Question 28

Write a formula for the general term, or nth term, for the given sequence.
$$1 , \frac { 2 } { 3 } , \frac { 1 } { 3 } , \frac { 2 } { 15 } , \ldots$$

A) $a _ { n } = \frac { 2 n } { ( n + 1 ) ! }$
B) $a _ { n } = \frac { 2 ^ { n + 1 } } { n ! }$
C) $a _ { n } = \frac { 2 ^ { n } } { n ! }$
D) $a _ { n } = \frac { 2 ^ { n } } { ( n + 1 ) ! }$

Question 29

The first several terms of a sequence are given. Find the indicated partial sum.
$$a _ { n } = ( - 1 ) ^ { n } ( 2 n ) ; s _ { 4 }$$

A)20
B)16
C)-20
D)4

Question 30

The general term of a sequence is given. Find the indicated partial sum.
$$a _ { 1 } = 4 , a _ { n } = a _ { n } - 1 + 6 \text { for } n \geq 2 ; S _ { 5 }$$

A)100
B)80
C)85
D)55

Question 31

Find the indicated term of the sequence.
$$- 7 , - 5 , - 3 , - 1 , \ldots ; S _ { 5 }$$

A)-35
B)75
C)-15
D)21

Question 32

The first several terms of a sequence are given. Find the indicated partial sum.
$$a _ { n } = \frac { ( - 1 ) ^ { n - 1 } } { 7 n } ; S _ { 4 }$$

A) $\frac { 25 } { 84 }$
B) $- \frac { 25 } { 84 }$
C) $\frac { 1 } { 12 }$
D) $- \frac { 1 } { 12 }$

Question 33

The general term of a sequence is given. Find the indicated partial sum.
$$\sum _ { i = 1 } ^ { 5 } \frac { ( \mathrm { i } + 2 ) ! } { ( \mathrm { i } + 1 ) ! }$$

A) 19
B) $\frac { 129 } { 20 }$
C) 25
D) $\frac { 377 } { 60 }$

Question 34

Find the sum of the series.
$$\sum _ { j = 1 } ^ { 4 } \left( j ^ { 2 } - 4 \right)$$

A) 14
B) 2
C) 30
D) 12

Question 35

Write a formula for the general term, or nth term, for the given sequence.
$$5,7,9,11 , \ldots ; \text { a }$$

A)19
B)15
C)17
D)5

Question 36

Write the first four terms of the recursive sequence.
$$\frac { 1 } { 9 } , \frac { 8 } { 9 } , \frac { 64 } { 9 } , \frac { 512 } { 9 } , \ldots$$

A) $a _ { n } = \frac { 8 n } { 9 }$
B) $a _ { n } = \frac { 8 n - 8 } { 9 }$
C) $a _ { n } = \frac { 8 ^ { n - 1 } } { 9 }$
D) $a _ { n } = \frac { 8 ^ { n } - 1 } { 9 }$

Question 37

Write a formula for the general term, or nth term, for the given sequence.
$$\frac { 2 } { 3 } , - \frac { 1 } { 3 } , \frac { 1 } { 6 } , - \frac { 1 } { 12 } , \ldots ; \mathrm { a } 6$$

A) $\frac { 1 } { 24 }$
B) $\frac { 1 } { 30 }$
C) $- \frac { 1 } { 96 }$
D) $- \frac { 1 } { 48 }$

Question 38

Find the sum of the series.
$$2 \left( 1 ^ { 2 } \right) + 2 \left( 2 ^ { 2 } \right) + \ldots + 2 \left( 6 ^ { 2 } \right)$$

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

Question 39

The first several terms of a sequence are given. Find the indicated partial sum.
$$2 , - 7,12 , - 17 , \ldots ; \mathrm { S } _ { 6 }$$

A)7
B)-15
C)-13
D)15

Question 40

The general term of a sequence is given. Find the indicated partial sum.
$$\sum _ { i = 5 } ^ { 8 } 5$$

A) 130
B) 20
C) 15
D) 105

Question 41

Rewrite the series using summation notation. Use 1 as the lower limit of summation.
$$a _ { n } = \frac { 7 n - 1 } { 8 }$$

A) yes, $- \frac { 1 } { 8 }$
B) yes, 7
C) yes, $\frac { 7 } { 8 }$
D) no

Question 42

Rewrite the series using summation notation. Use 1 as the lower limit of summation.
-9 , -11 , -13 , -15 , . . .

A)no
B)yes, -4
C)yes, -6
D)yes, -2

Question 43

Find the general term of the arithmetic sequence.
$\frac { 5 } { 9 } , \frac { 2 } { 3 } , \frac { 7 } { 9 } , \ldots ; a _ { 16 }$

A) $\frac { 20 } { 9 }$
B) $\frac { 19 } { 9 }$
C) $\frac { 17 } { 9 }$
D) 2

Question 44

Find the sum of the series.
$$\frac { 1 } { 3 } + \frac { 1 } { 2 } + \frac { 3 } { 5 } + \ldots + \frac { 7 } { 8 }$$

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

Question 45

Find the sum of the series.
$$- \frac { 1 } { 3 } + \frac { 1 } { 6 } - \frac { 1 } { 9 } + \ldots - \frac { 1 } { 21 }$$

A) $\sum _ { \mathrm { i } = 1 } ^ { 7 } \frac { ( - 1 ) ^ { \mathrm { i } } } { 3 \mathrm { i } }$
B) $\sum _ { i = 1 } ^ { 7 } \frac { ( - 1 ) ^ { i } } { 3 ^ { i } }$
C) $\sum _ { i = 1 } ^ { 7 } \frac { ( - 1 ) ^ { i - 1 } } { 3 i }$
D) $\sum _ { i = 1 } ^ { 7 } \frac { ( - 1 ) ^ { i - 1 } } { 3 ^ { i } }$

Question 46

Find the general term of the arithmetic sequence.
$$\frac { 1 } { 6 } , \frac { 2 } { 3 } , \frac { 7 } { 6 } , \frac { 5 } { 3 } , \frac { 13 } { 6 } , \ldots$$

A) $a _ { n } = \frac { n - 2 } { 6 }$
B) $a _ { n } = \frac { n + 1 } { 6 }$
C) $a _ { n } = \frac { 3 n + 1 } { 6 }$
D) $a _ { n } = \frac { 3 n - 2 } { 6 }$

Question 47

Rewrite the series using summation notation. Use 1 as the lower limit of summation.
$$2 ^ { 2 } + 4 ^ { 3 } + 6 ^ { 4 } + \ldots + 16 ^ { 9 }$$

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

Question 48

Determine if the sequence is arithmetic. If the sequence is arithmetic, find the common difference.
$$a _ { 1 } = - 3 , a _ { n } = 3 a _ { n - 1 }- 4$$

A)yes, -4
B)no
C)yes, 4
D)yes, 3

Question 49

Find the general term of the arithmetic sequence.
6 , 15 , 24 , 33 , 42 , . . . ; $$\text { a20 }$$

A)51
B)59
C)179
D)177

Question 50

Rewrite the series using summation notation. Use 1 as the lower limit of summation.
$$a _ { 1 } = 2 , a _ { n } = a _ { n - 1 } + 8$$

A)yes, 1
B)yes, 2
C)yes, 8
D)no

Question 51

Find the general term of the arithmetic sequence.
7, 2 , -3, -8, . . . ; $$a _ { 20 }$$

A)-88
B)88
C)93
D)-93

Question 52

Rewrite the series using summation notation. Use 1 as the lower limit of summation.
7 , 11 , 15 , 19 , . . .

A)no
B)yes, -4
C)yes, 4
D)yes, 12

Question 53

Find the sum of the series.
$$2 + 4 + 6 + \ldots + 18$$

A) $\sum _ { i = 1 } ^ { 9 } 2 ( \mathrm { i } - 1 )$
B) $\sum _ { i = 1 } ^ { 9 } 2 i$
C) $\sum _ { i = 1 } ^ { 9 } 2$
D) $\sum _ { i = 1 } ^ { 9 } \mathrm { i } + 2$

Question 54

Rewrite the series using summation notation. Use 1 as the lower limit of summation.
3 , 9 , 27 , 81 , 243, . . .

A)yes, 3 $$\text { B) yes, } \frac { 1 } { 3 }$$
C)no
D)yes, 9

Question 55

Find the sum of the series.
$$3 + \frac { 3 ^ { 2 } } { 2 } + \frac { 3 ^ { 3 } } { 3 } + \ldots + \frac { 3 ^ { n } } { n }$$

A) $\sum _ { i = 1 } ^ { n } \frac { 3 ^ { n } } { i }$
B) $\sum _ { i = 1 } ^ { n } \frac { 3 i } { i }$
C) $\sum _ { i = 1 } ^ { n } \frac { 3 ^ { i } } { i }$
D) $\sum _ { i = 1 } ^ { 3 } \frac { 3 ^ { i } } { i }$

Question 56

Determine if the sequence is arithmetic. If the sequence is arithmetic, find the common difference.
$3,9,15,21,27 , \ldots$

A) $a _ { n } = 6 n - 1$
B) $a _ { n } = 3 ( 6 ) ^ { n - 1 }$
C) $a _ { n } = 3 n - 6$
D) $a _ { n } = 6 n - 3$

Question 57

Determine if the sequence is arithmetic. If the sequence is arithmetic, find the common difference.
$6.9,7.7,8.5,9.3,10.1 , \ldots$

A) $a _ { n } = 0.8 n + 6.1$
B) $a _ { n } = 0.7 n + 6.1$
C) $a _ { n } = 0.8 n + 5.9$
D) $a _ { n } = 0.8 n + 6.9$

Question 58

Rewrite the series using summation notation. Use 1 as the lower limit of summation.
an = n(n - 3)

A)yes, 1
B)yes, 3
C)no
D)yes, -3

Question 59

Determine if the sequence is arithmetic. If the sequence is arithmetic, find the common difference.
$- 1 , - 7 , - 13 , - 19 , - 25 , \ldots$

A) $a _ { n } = - 11 - 6 n$
B) $a _ { n } = 5 - 6 n$
C) $a _ { n } = 6 n - 5$
D) $a _ { n } = - 5 - 6 n$

Question 60

Find the general term of the arithmetic sequence.
6.1, 5.5, 4.9, . . . ; $$\text { a9 }$$

A)1.9
B)1.31
C)1.3
D)0.7

Question 61

Solve the problem.
If a person puts 1 cent in a piggy bank on the first day, 2 cents on the second day, 3 cents on the third day, and so on, how much money will be in the bank after 60 days?

A)$36.60
B)$18.30
C)$0.60
D)$9.15

Question 62

Find the general term of the arithmetic sequence then find the indicated term of the sequence. Assume that the domain of the sequence is all natural numbers.
3 + 6 + 9 + . . . + 120

A)4797
B)2460
C)2398
D)4920

Question 63

Solve the problem.
A collection of dimes is arranged in a triangular array with 15 coins in the base row, 14 in the next, 13 in the next, and so on with 1 dime in the last row. Find the value of the collection.

A)$1.20
B)$24.00
C)$12.00
D)$6.00

Question 64

Find the general term of the arithmetic sequence then find the indicated term of the sequence. Assume that the domain of the sequence is all natural numbers.
Find the sum of the first 837 even positive integers.

A)699,732
B)701,406
C)702,244
D)700,569

Question 65

Find the general term of the arithmetic sequence.
Given an arithmetic sequence with d $$\mathrm { d } = - 6 \text { and } \mathrm { a } _ { 4 } = 10$$ find a20.

A)86
B)-86
C)-92
D)92

Question 66

Find the general term of the arithmetic sequence then find the indicated term of the sequence. Assume that the domain of the sequence is all natural numbers.
$$\sum _ { n = 1 } ^ { 37 } ( 2 n - 4 )$$

A) 1258
B) 1221
C) 1480
D) $1350.5$

Question 67

Find the general term of the arithmetic sequence.
Given an arithmetic sequence with d = 6 and a5 = 27 , find a20.

A)119
B)59
C)54
D)117

Question 68

Find the indicated term of the arithmetic sequence.
Find $a _ { n }$ and $a _ { 8 }$ .

A) $a _ { n } = n + 1 ; a _ { 8 } = 9$
B) $a _ { n } = n - 2 ; a _ { 8} = 6$
C) $a _ { n } = n + 2 ; a _ { 8 } = 10$
D) $a _ { n } = n - 1 ; a _ { 8 } = 7$

Question 69

Find the general term of the arithmetic sequence then find the indicated term of the sequence. Assume that the domain of the sequence is all natural numbers.
-3 + 1 + 5 + 9 + 13 + . . . + (4n - 7)

A)n(4n - 7)
B)n(4n + 7)
C)n(2n - 5)
D)n(2n + 5)

Question 70

Find the general term of the arithmetic sequence then find the indicated term of the sequence. Assume that the domain of the sequence is all natural numbers.
$$\sum _ { n = 1 } ^ { 42 } ( - 3 n - 3 )$$

A) $- 2541$
B) $- 2835$
C) $- 2772$
D) $- 2688$

Question 71

Find the general term of the arithmetic sequence then find the indicated term of the sequence. Assume that the domain of the sequence is all natural numbers.
7 + 3 - 1 + . . . - 153

A)-144
B)-2993
C)-2920
D)-146

Question 72

Find the general term of the arithmetic sequence then find the indicated term of the sequence. Assume that the domain of the sequence is all natural numbers.
$$\frac { 1 } { 5 } + 1 + \frac { 9 } { 5 } + \ldots + 9$$

A) $\frac { 552 } { 5 }$
B) $\frac { 253 } { 5 }$
C) 66
D) $\frac { 276 } { 5 }$

Question 73

Find the general term of the arithmetic sequence then find the indicated term of the sequence. Assume that the domain of the sequence is all natural numbers.
$$\sum _ { n = 1 } ^ { 38 } ( 6 n + 5 )$$

A) 4522
B) 4940
C) 4636
D) 4807

Question 74

Find the indicated term of the arithmetic sequence.
Find $a _ { n }$ and $a _ { 21 }$ .

A) $a _ { n } = n + 3 ; a _ { 21 } = 24$
B) $a _ { n } = 4 - n ; a _ { 21 } = - 17$
C) $a _ { n } = n - 4 ; a _ { 21 } = 17$
D) $a _ { n } = n + 2 ; a _ { 21 } = 23$

Question 75

Find the general term of the arithmetic sequence then find the indicated term of the sequence. Assume that the domain of the sequence is all natural numbers.
-20 + -30 + -40 + -50 + . . . + a40

A)-8595
B)-8800
C)-8600
D)-420

Question 76

Find the general term of the arithmetic sequence then find the indicated term of the sequence. Assume that the domain of the sequence is all natural numbers.
19 + 24 + 29 + 34 + . . . + a60

A)319
B)10,140
C)9998
D)9990

Question 77

Find the indicated term of the arithmetic sequence.
Given an arithmetic sequence with a16 = 19 and a10 = 7, find a4.

A)-3
B)-11
C)-5
D)2

Question 78

Find the general term of the arithmetic sequence.
Given an arithmetic sequence with a1 = -8 and a8 = 48, find a15.

A)85
B)54
C)112
D)104

Question 79

Find the general term of the arithmetic sequence then find the indicated term of the sequence. Assume that the domain of the sequence is all natural numbers.
Find an and a35.

A) $a _ { n } = n + 2 ; a _ { 35 } = 37$
B) $a _ { n } = 3 - n ; a _ { 35 } = - 32$
C) $a _ { n } = n + 1 ; a _ { 35 } = 36$
D) $a _ { n } = n - 3 ; a _ { 35 } = 32$

Question 80

Find the indicated term of the arithmetic sequence.
Find $a _ { n }$ and $a _ { 18 }$ .

A) $a _ { n } = n - 4 ; a _ { 18 } = 14$
B) $a _ { n } = n + 4 ; a _ { 18 } = 23$
C) $a _ { n } = n + 3 ; a _ { 18 } = 21$
D) $a _ { n } = n - 3 ; a _ { 18 } = 15$