Deck 52: Sequences and Series

Question 1

Select the first five terms of the sequence.(Assume that n begins with 1. )​ $$a _ { n } = 5 n - 6$$ ​

A) $0 , - 1,4,9,14$
B) $- 1,4,9,14,19$
C) $5 , - 1,15,9,25$
D) $5,10,15,20,25$
E) $5,4,15,14,25$

Answer 1

$- 1,4,9,14,19$

Question 2

Select the first five terms of the sequence.(Assume that n begins with 1. )​ $$a _ { n } = n ( n - 2 ) ( n - 3 )$$ ​

A) $30,2,0,0,8$ ​
B) $0,0,8,30,2$ ​
C) $2,0,0,8,30$ ​
D) $8,30,2,0,0$ ​
E) $0,8,30,2,0$ ​

Answer 2

$2,0,0,8,30$ ​

Question 3

Find the indicated term of the sequence.​ $$\begin{array} { l } a _ { n } = ( - 1 ) ^ { n } ( 6 n - 5 ) \\a _ { 15 } =\end{array}$$ ​

A)85
B)-92
C)-85
D)-84
E)95

Answer 3

-85

Question 4

Select the first five terms of the sequence.(Assume that n begins with 1. )​ $$a _ { n } = ( - 5 ) ^ { n }$$ ​

A) $$- 5,25 , - 15,625 , - 25$$
B) $$- 5,25 , - 125,625 , - 3125$$
C) $1 , - 5,25 , - 125,625$
D) $- 5 , - 10 , - 15 , - 125 , - 25$
E) $- 5 , - 10 , - 15 , - 20 , - 25$

Question 5

Find the indicated term of the sequence.​ $$\begin{aligned}a _ { n } & = \frac { 5 n } { 3 n ^ { 2 } - 4 } \\a _ { 11 } & =\end{aligned}$$ ​

A) $- \frac { 359 } { 55 }$
B) $\frac { 359 } { 55 }$
C) $- \frac { 55 } { 359 }$
D) $\frac { 55 } { 359 }$
E) $\frac { 55 } { 367 }$

Question 6

Select the first five terms of the sequence.(Assume that n begins with 1. )​ $$a _ { n } = \frac { 8 } { 5 }$$ ​

A) $- \frac { 8 } { 5 } , - \frac { 8 } { 5 } , - \frac { 8 } { 5 } , - \frac { 8 } { 5 } , - \frac { 8 } { 5 }$ ​
B) $- \frac { 5 } { 8 } , \frac { 5 } { 8 } , - \frac { 5 } { 8 } , \frac { 5 } { 8 } , - \frac { 5 } { 8 }$ ​
C) $\frac { 8 } { 5 } , \frac { 8 } { 5 } , \frac { 8 } { 5 } , \frac { 8 } { 5 } , \frac { 8 } { 5 }$ ​
D)0,1,2,3,4
E) $\frac { 5 } { 8 } , \frac { 5 } { 8 } , \frac { 5 } { 8 } , \frac { 5 } { 8 } , \frac { 5 } { 8 }$ ​

Question 7

Find the sum.​ $$\sum _ { i = 1 } ^ { 5 } 6 i ^ { 2 }$$ ​

A)150
B)300
C)210
D)270
E)330

Question 8

Select the first five terms of the sequence.(Assume that n begins with 1. )​ $$a _ { n } = \frac { n } { n + 7 }$$ ​

A) $- 8 , \frac { 9 } { 2 } , - \frac { 10 } { 3 } , \frac { 11 } { 4 } , - \frac { 12 } { 5 }$ ​
B) $8 , - \frac { 9 } { 2 } , - \frac { 10 } { 3 } , - \frac { 11 } { 4 } , - \frac { 12 } { 5 }$ ​
C) $8 , \frac { 9 } { 2 } , \frac { 10 } { 3 } , \frac { 11 } { 4 } , \frac { 12 } { 5 }$ ​
D) $\frac { 1 } { 8 } , \frac { 2 } { 9 } , \frac { 3 } { 10 } , \frac { 4 } { 11 } , \frac { 5 } { 12 }$ ​
E) $0 , \frac { 1 } { 8 } , \frac { 2 } { 9 } , \frac { 3 } { 10 } , \frac { 4 } { 11 }$ ​

Question 9

Select the first five terms of the sequence.​ $$a _ { n } = 2 - \frac { 1 } { 5 ^ { n } }$$ ​

A) $\frac { 9 } { 125 } , \frac { 49 } { 25 } , \frac { 249 } { 5 } , \frac { 1249 } { 25 } , \frac { 6249 } { 125 }$
B) $\frac { 9 } { 25 } , \frac { 49 } { 125 } , \frac { 249 } { 625 } , \frac { 1249 } { 3125 } , \frac { 6249 } { 5 }$
C) $\frac { 5 } { 9 } , \frac { 25 } { 49 } , \frac { 125 } { 249 } , \frac { 625 } { 1249 } , \frac { 3125 } { 6249 }$
D) $\frac { 49 } { 5 } , \frac { 249 } { 25 } , \frac { 1249 } { 125 } , \frac { 6249 } { 625 } , \frac { 9 } { 3125 }$
E) $\frac { 9 } { 5 } , \frac { 49 } { 25 } , \frac { 249 } { 125 } , \frac { 1249 } { 625 } , \frac { 6249 } { 3125 }$

Question 10

Select the first five terms of the sequence.(Assume that n begins with 1. ) $$a _ { n } = 7 + ( - 7 ) ^ { n }$$ ​

A) $7,0,56 , - 336,2408$
B) $0,56 , - 336,2408 , - 16800$
C) $1,56 , - 334,2408 , - 16803$
D) $0,55 , - 336,2406 , - 16800$
E) $1,55 , - 334,2406 , - 16803$

Question 11

Write an expression for the apparent nth term of the sequence.(Assume that n begins with 1. )​ $$1,7,13,19,25 , \ldots$$ ​

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

Question 12

Select the first five terms of the sequence.(Assume that n begins with 1. )​ $$a _ { n } = ( - 1 ) ^ { n } \left( \frac { n } { n + 11 } \right)$$ ​

A) $\frac { 1 } { 12 } , \frac { 2 } { 13 } , \frac { 3 } { 14 } , \frac { 4 } { 15 } , \frac { 5 } { 16 }$ ​
B) $- \frac { 1 } { 12 } , - \frac { 2 } { 13 } , - \frac { 3 } { 14 } , - \frac { 4 } { 15 } , - \frac { 5 } { 16 }$ ​
C) $- \frac { 1 } { 12 } , \frac { 2 } { 13 } , \frac { 3 } { 14 } , \frac { 4 } { 15 } , - \frac { 5 } { 16 }$ ​
D) $- 12 , - \frac { 2 } { 13 } , - \frac { 3 } { 14 } , \frac { 4 } { 15 } , - \frac { 5 } { 16 }$ ​
E) $- \frac { 1 } { 12 } , \frac { 2 } { 13 } , - \frac { 3 } { 14 } , \frac { 4 } { 15 } , - \frac { 5 } { 16 }$ ​

Question 13

Select the first five terms of the sequence.(Assume that n begins with 1. )​ $$a _ { n } = \left( \frac { 1 } { 5 } \right) ^ { n }$$ ​

A) $$\frac { 1 } { 5 } , \frac { 1 } { 10 } , \frac { 1 } { 15 } , \frac { 1 } { 125 } , \frac { 1 } { 25 }$$
B) $$\frac { 1 } { 5 } , \frac { 1 } { 10 } , \frac { 1 } { 125 } , \frac { 1 } { 20 } , \frac { 1 } { 3125 }$$
C) $\frac { 1 } { 5 } , \frac { 1 } { 25 } , \frac { 1 } { 125 } , \frac { 1 } { 625 } , \frac { 1 } { 3125 }$
D) $\frac { 1 } { 5 } , \frac { 1 } { 10 } , \frac { 1 } { 15 } , \frac { 1 } { 20 } , \frac { 1 } { 25 }$
E) $1 , \frac { 1 } { 5 } , \frac { 1 } { 25 } , \frac { 1 } { 125 } , \frac { 1 } { 625 }$

Question 14

Select the first five terms of the sequence.(Assume that n begins with 1. )​ $$a _ { n } = \frac { n + 11 } { n }$$ ​

A) $11,12 , \frac { 13 } { 2 } , \frac { 14 } { 3 } , \frac { 15 } { 4 }$
B) $- 12 , \frac { 13 } { 2 } , - \frac { 14 } { 3 } , \frac { 15 } { 4 } , - \frac { 16 } { 5 }$
C) $12 , - \frac { 13 } { 2 } , - \frac { 14 } { 3 } , - \frac { 15 } { 4 } , - \frac { 16 } { 5 }$
D) $12 , \frac { 13 } { 2 } , \frac { 14 } { 3 } , \frac { 15 } { 4 } , \frac { 16 } { 5 }$
E) $\frac { 1 } { 12 } , \frac { 1 } { 13 } , \frac { 1 } { 14 } , \frac { 1 } { 15 } , \frac { 1 } { 16 }$

Question 15

Select the first five terms of the sequence.(Assume that n begins with 1. )​ $$a _ { n } = 4 ^ { n }$$ ​

A) $1,4,16,64,256$ ​
B) $$4,8,64,16,1024$$ ​
C) $$4,16,64,256,1024$$ ​
D) $4,8,12,16,20$ ​
E) $4,8,12,64,20$ ​

Question 16

Select the first five terms of the sequence.(Assume that n begins with 1. )​ $$a _ { n } = \frac { 50 } { n ^ { 2 / 3 } }$$ ​

A) $$- 50 , \frac { 50 } { \sqrt [ 3 ] { 4 } } , - \frac { 50 } { \sqrt [ 3 ] { 9 } } , \frac { 50 } { \sqrt [ 3 ] { 16 } } , - \frac { 50 } { \sqrt [ 3 ] { 25 } }$$ ​
B) $$50 , - \frac { 50 } { \sqrt [ 3 ] { 4 } } , \frac { 50 } { \sqrt [ 3 ] { 9 } } , - \frac { 50 } { \sqrt [ 3 ] { 16 } } , \frac { 50 } { \sqrt [ 3 ] { 25 } }$$ ​
C) $50 , \frac { 50 } { \sqrt [ 3 ] { 4 } } , \frac { 50 } { \sqrt [ 3 ] { 9 } } , \frac { 50 } { \sqrt [ 3 ] { 16 } } , \frac { 50 } { \sqrt [ 3 ] { 25 } }$ ​
D) $- 50 , \frac { 50 } { \sqrt [ 3 ] { 2 } } , - \frac { 50 } { \sqrt [ 3 ] { 3 } } , \frac { 50 } { \sqrt [ 3 ] { 4 } } , - \frac { 50 } { \sqrt [ 3 ] { 5 } }$ ​
E) $50 , \frac { 50 } { \sqrt [ 3 ] { 2 } } , \frac { 50 } { \sqrt [ 3 ] { 3 } } , \frac { 50 } { \sqrt [ 3 ] { 4 } } , \frac { 50 } { \sqrt [ 3 ] { 5 } }$ ​

Question 17

Select the first five terms of the sequence.(Assume that n begins with 1. )​ $$a _ { n } = n \left( n ^ { 2 } - 8 \right)$$ ​

A) $32,85 , - 7 , - 8,3$ ​
B) $- 7 , - 8,3,32,85$ ​
C) $3,32,85 , - 7 , - 8$ ​
D) $- 8,3,32,85 , - 7$ ​
E) $85 , - 7 , - 8,3,32$ ​

Question 18

Select the first five terms of the sequence.(Assume that n begins with 1. )​ $$a _ { n } = \frac { 8 ^ { n } } { 3 ^ { n } }$$ ​

A) $\frac { 8 } { 27 } , \frac { 64 } { 9 } , \frac { 512 } { 3 } , \frac { 4,096 } { 9 } , \frac { 32,768 } { 27 }$ ​
B)​ $\frac { 8 } { 9 } , \frac { 64 } { 27 } , \frac { 512 } { 81 } , \frac { 4,096 } { 243 } , \frac { 32,768 } { 3 }$
C) $\frac { 64 } { 3 } , \frac { 512 } { 9 } , \frac { 4,096 } { 27 } , \frac { 32,768 } { 81 } , \frac { 8 } { 243 }$ ​ ​
D) $\frac { 3 } { 8 } , \frac { 9 } { 64 } , \frac { 27 } { 512 } , \frac { 81 } { 4,096 } , \frac { 243 } { 32,768 }$ ​
E) $\frac { 8 } { 3 } , \frac { 64 } { 9 } , \frac { 512 } { 27 } , \frac { 4,096 } { 81 } , \frac { 32,768 } { 243 }$ ​

Question 19

Select the first five terms of the sequence.(Assume that n begins with 1. )​ $$a _ { n } = \left( - \frac { 1 } { 3 } \right) ^ { n }$$ ​

A) $- \frac { 1 } { 3 } , \frac { 1 } { 9 } , - \frac { 1 } { 27 } , \frac { 1 } { 81 } , - \frac { 1 } { 243 }$
B) $$- \frac { 1 } { 3 } , - \frac { 1 } { 6 } , \frac { 1 } { 27 } , \frac { 1 } { 12 } , - \frac { 1 } { 243 }$$
C) $$- \frac { 1 } { 3 } , \frac { 1 } { 6 } , - \frac { 1 } { 9 } , \frac { 1 } { 27 } , - \frac { 1 } { 15 }$$
D) $\frac { 1 } { 3 } , - \frac { 1 } { 6 } , \frac { 1 } { 9 } , - \frac { 1 } { 12 } , \frac { 1 } { 15 }$
E) $- \frac { 1 } { 3 } , \frac { 1 } { 9 } , - \frac { 1 } { 9 } , \frac { 1 } { 81 } , - \frac { 1 } { 15 }$

Question 20

Select the first five terms of the sequence.(Assume that n begins with 1. )​ $$a _ { n } = 3 n + 6$$ ​

A) $3,12,9,18,15$ ​
B) $3,9,9,15,15$ ​
C) $3,6,9,12,15$ ​
D) $0,9,12,12,18$ ​
E) $9,12,15,18,21$ ​

Question 21

Find the sum of the infinite series.​ $$\sum _ { j = 1 } ^ { \infty } \left( \frac { 7 } { 10 } \right) ^ { j }$$ ​

A) $- \frac { 7 } { 3 } j$ ​
B) $\frac { 7 } { 3 }$ ​
C) $- \frac { 7 } { 10 } j$
D) $\frac { 7 } { 10 }$
E) $- \frac { 7 } { 3 }$ ​

Question 22

Find the indicated term of the sequence. $a _ { n } = ( - 1 ) ^ { n } ( 4 n - 1 )$ $a _ { 14 } =$ $\square$

A)57
B)52
C)-3
D)55
E)-51

Question 23

Write an expression for the apparent nth term of the sequence.(Assume that n begins with 1. )​ $$2,6,10,14,18 , \ldots$$ ​

A) $$a _ { n } = 2 n - 4$$
B) $a _ { n } = 4 n - 2$
C) $$a _ { n } = 2 n + 4$$
D) $a _ { n } = - 4 n - 2$
E) $a _ { n } = 4 n + 2$

Question 24

Use sigma notation to write the sum.​ $$\frac { 1 } { 3 ( 1 ) } + \frac { 1 } { 3 ( 2 ) } + \frac { 1 } { 3 ( 3 ) } + \ldots + \frac { 1 } { 3 ( 9 ) }$$ ​

A) $\sum _ { i = 1 } ^ { 9 } - \frac { 1 } { 3 i }$
B) $\sum _ { i = 0 } ^ { 10 } \frac { 1 } { 3 i }$
C) $\sum _ { i = 1 } ^ { 9 } 3 i$
D) $\sum _ { i = 1 } ^ { 9 } \frac { 1 } { 3 i }$
E) $\sum _ { i = 1 } ^ { - 9 } \frac { 1 } { 3 i }$

Question 25

Select the first five terms of the sequence defined recursively.​ $$a _ { 1 } = 54 , a _ { k + 1 } = a _ { k } - 2$$ ​

A) $56,58,60,62,64$ ​
B) $52,58,50,62,64$
C) $56,52,60,48,64$
D) $54,58,50,62,46$
E) $54,52,50,48,46$

Question 26

Find the sum.​ $$\sum _ { i = 1 } ^ { 5 } ( 6 i + 1 )$$ ​

A)85
B)35
C)26
D)95
E)55

Question 27

Write an expression for the apparent nth term of the sequence.(Assume that n begins with 1. )​ $$- 243,729 , - 2187,6561 , - 19683 , \ldots$$ ​

A) $a _ { n } = 3 ^ { n - 4 }$ ​
B) $a _ { n } = ( - 3 ) ^ { n - 4 }$ ​
C) $a _ { n } = 3 ^ { n + 4 }$ ​
D) $a _ { n } = ( - 3 ) ^ { n }$ ​
E) $a _ { n } = ( - 3 ) ^ { n + 4 }$ ​

Question 28

Write an expression for the apparent nth term of the sequence.(Assume that n begins with 1. ) $5 - \frac { 2 } { 1 } , 5 - \frac { 2 } { 2 } , 5 - \frac { 2 } { 3 } , 5 - \frac { 2 } { 4 } , 5 - \frac { 2 } { 5 }$ ,

A) $a _ { n } = 5 - \frac { 2 } { n + 1 }$
B) $$a _ { n } = 2 - \frac { n } { 5 }$$
C) $$a _ { n } = 5 - \frac { n } { 2 }$$
D) $a _ { n } = 2 - \frac { 5 } { n }$
E) $a _ { n } = 5 - \frac { 2 } { n }$

Question 29

Write an expression for the apparent nth term of the sequence.(Assume that n begins with 1. )​ $$2 , - 4,6 , - 8,10 , \ldots$$ ​

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

Question 30

Find the sum of the infinite series.​ $$\sum _ { i = 1 } ^ { \infty } 4 \left( \frac { 1 } { 10 } \right) ^ { i }$$ ​

A) $\frac { 4 i } { 9 }$
B) $\frac { 4 } { 9 }$
C) $\frac { 9 i } { 4 }$
D) $- \frac { 4 i } { 9 }$
E) $\frac { 9 } { 4 }$

Question 31

Write an expression for the apparent nth term of the sequence.(Assume that n begins with 1. )​ $$- 2,1,6,13,22 , \ldots$$ ​

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

Question 32

Find the sum.​ $$\sum _ { i = 1 } ^ { 4 } 50$$ ​

A)200
B)199
C)210
D)201
E)150

Question 33

Select the first five terms of the sequence defined recursively.​ $$a _ { 1 } = 23 , a _ { k + 1 } = a _ { k } + 3$$ ​

A) $$23,26,29,32,35$$ ​
B) $$26,17,29,11,8$$ ​
C) $20,26,14,32,8$ ​
D) $20,17,14,11,8$ ​
E) $23,17,29,11,35$ ​

Question 34

Write an expression for the apparent nth term of the sequence.(Assume that n begins with 1. )​ $$\frac { 2 } { 7 } , \frac { 3 } { 15 } , \frac { 4 } { 23 } , \frac { 5 } { 31 } , \frac { 6 } { 39 } , \ldots$$ ​

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

Question 35

Select the first five terms of the sequence defined recursively.Use the pattern to write the nth term of the sequence as a function of n.(Assume that n begins with 1. )​ $$a _ { 1 } = 9 , a _ { k + 1 } = a _ { k } + 3$$ ​

A) $\begin{array} { l } 9,12,15,18,21 \\a _ { n } = 3 n + 3\end{array}$
B) $\begin{array} { l } 9,12,15,18,21 \\a _ { n } = 6 n + 3\end{array}$
C) $\begin{array} { l } 9,12,15,18,21 \\a _ { n } = 3 n + 6\end{array}$
D) $\begin{array} { l } 9,12,15,18,21 \\a _ { n } = 6 n - 3\end{array}$
E) $\begin{array} { l } 9,12,15,18,21 \\a _ { n } = 3 n - 6\end{array}$

Question 36

Write an expression for the apparent nth term of the sequence.(Assume that n begins with 1. )​ $$3,5,3,5,3 , \ldots$$ ​

A) $a _ { n } = ( - 1 ) ^ { n } + 4$
B) $a _ { n } = ( - 1 ) ^ { n + 1 }$
C) $a _ { n } = ( - 1 ) ^ { n } - 4$
D) $a _ { n } = 4 ^ { n } - 1$
E) $a _ { n } = ( - 1 ) ^ { n - 1 } + 4$

Question 37

Write the first five terms of the sequence.(Assume that n begins with 1. ) $$a _ { n } = - n - 2$$

A)-3,-2,-3,-4,-5
B)-2,-3,-4,-5,-6
C)-3,-4,-5,-6,-7
D)-3,-5,-7,-9,-11
E)1,0,-2,-2,-3

Question 38

Write an expression for the apparent nth term of the sequence.(Assume that n begins with 1. )​ $$\frac { 1 } { 5 } , \frac { 4 } { 25 } , \frac { 16 } { 125 } , \frac { 64 } { 625 }$$ ​

A) $a _ { n } = \frac { 4 ^ { n - 1 } } { 5 ^ { n } }$
B) $a _ { n } = \frac { 4 ^ { n - 1 } } { 5 ^ { n - 1 } }$
C) $a _ { n } = \frac { 4 ^ { n + 1 } } { 5 ^ { n + 1 } }$
D) $a _ { n } = \frac { 4 ^ { n } } { 5 ^ { n } }$
E) $a _ { n } = \frac { 4 ^ { n + 1 } } { 5 ^ { n } }$

Question 39

Find the sum of the infinite series.​ $$\sum _ { i = 1 } ^ { \infty } 2 \left( \frac { 1 } { 10 } \right) ^ { i }$$ ​

A) $\frac { 2 } { 9 }$ ​
B) $\frac { 9 k } { 2 }$ ​
C) $\frac { 9 } { 2 }$ ​
D) $- \frac { 2 k } { 9 }$ ​
E) $\frac { 2 k } { 9 }$ ​

Question 40

Write an expression for the apparent nth term of the sequence.(Assume that n begins with 1. ) 3,8,13,18,23

A) $a _ { n } = - 2 n + 5$
B) $a _ { n } = ( - 1 ) ^ { n } ( 5 n - 2 )$
C) $a _ { n } = 5 n$
D) $a _ { n } = 5 ^ { n } - 2$
E) $a _ { n } = 5 n - 2$

Question 41

Write the first five terms of the sequence defined recursively.Use the pattern to write the nth term of the sequence as a function of n.(Assume that n begins with 1. ) $$a _ { 1 } = - 7 , a _ { k + 1 } = 3 a _ { k }$$

A) $a _ { n } = - 7 n ; - 7 , - 21 , - 63 , - 189 , - 567$ ​
B) $$a _ { n } = - 7 ( 3 ) ^ { n } ; - 21 , - 63 , - 189 , - 567 , - 1701$$ ​
C) $a _ { n } = ( - 21 ) ^ { n } ; - 7 , - 63 , - 189 , - 567 , - 1701$ ​
D) $a _ { n } = ( - 21 ) ^ { n - 1 } ; - 21 , - 63 , - 189 , - 567 , - 1701$ ​
E) $a _ { n } = - 7 ( 3 ) ^ { n - 1 } ; - 7 , - 21 , - 63 , - 189 , - 567$ ​

Question 42

Find the sum. $$\sum _ { i = 1 } ^ { 4 } - i + 5$$

A)1
B)15
C)10
D)-10
E)9

Question 43

Find the sum. $$\sum _ { k = 1 } ^ { 3 } \frac { 1 } { k ^ { 2 } + 5 }$$

A) $\frac { 73 } { 168 }$ ​
B) $\frac { 1 } { 14 }$
C) $\frac { 22 } { 63 }$ ​
D)1
E) $\frac { 12 } { 11 }$ ​

Question 44

Evaluate the sum.​ $$\sum _ { k = 1 } ^ { 400 } 7$$ ​

A)4
B)400
C)2,805
D)2,800
E)7

Question 45

Write the first five terms of the sequence.(Assume that n begins with 1. ) $$a _ { n } = - 8 n + 8$$

A)-16,-24,-40,-40,-48
B)8,0,-8,-16,-24
C)0,-16,-24,-32,-40
D)0,-8,-16,-24,-32
E)0,8,16,24,32

Question 46

Write the first five terms of the sequence defined recursively.Use the pattern to write the nth term of the sequence as a function of n.(Assume that n begins with 1. ) $$a _ { 1 } = - 8 , a _ { k + 1 } = - 3 a _ { k }$$

A) $$a _ { k } = ( 24 ) ^ { n } ; - 8 , - 512,4096 , - 32768,262144$$ ​
B) $a _ { n } = - 8 ( - 3 ) ^ { n - 1 } ; - 8,24 , - 72,216 , - 648$ ​
C) $$a _ { n } = - 8 n ; - 8 , - 16 , - 24 , - 32 , - 40$$ ​
D) $a _ { k } = ( 24 ) ^ { n - 1 } ; - 8 , - 512,4096 , - 32768,262144$ ​
E) $a _ { n } = - 8 ( - 3 ) ^ { n } ; 24 , - 72,216 , - 648,1944$ ​

Question 47

Write the first six terms of the sequence defined by the function. f(n)= 3n(n - 1)

A)0,6,18,36,60,90
B)-6,0,18,36,60,90
C)6,18,36,60,90,252
D)-6,-18,36,-60,-90,0
E)6,18,36,60,90,126

Question 48

Find the next term of the sequence. 7,13,19,25,...

A)62
B)27
C)31
D)37
E)34

Question 49

Write the first five terms of the sequence defined recursively.Use the pattern to write the nth term of the sequence as a function of n.(Assume that n begins with 1. ) $$a _ { 1 } = 7 , a _ { k + 1 } = a _ { k } - 1$$

A) $a _ { n } = 8 - n ; 7,6,5,4,3$ ​
B) $a _ { n } = 7 ; 7,7,7,7,7$ ​
C) $a _ { n } = 9 - n ; 6,5,4,3,2$ ​
D) $a _ { n } = 8 n ; 7,21,28,35,42$ ​
E) $a _ { n } = 7 ( n - 1 ) ; 7,14,21,28,35$ ​

Question 50

Write an expression for the apparent nth term of the sequence.(Assume that n begins with 1. ) 2,7,12,17,22

A) $a _ { n } = - 3 n + 5$
B) $a _ { n } = ( - 1 ) ^ { n } ( 5 n - 3 )$
C) $a _ { n } = 5 n$
D) $a _ { n } = 5 ^ { n } - 3$
E) $a _ { n } = 5 n - 3$

Question 51

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

A) $\frac { 3 } { 4 }$
B) $- \frac { 17 } { 12 }$ ​
C) $\frac { 11 } { 4 }$ ​
D) $\frac { 1 } { 4 }$ ​
E) $- \frac { 5 } { 4 }$ ​

Question 52

A deposit of $ 5000 is made in an account that earns 4 % interest compounded quarterly.The balance in the account after n quarters is given by $$A _ { n } = 5000 \left( 1 + \frac { 0.04 } { 4 } \right) ^ { n } , n = 1,2,3 , \ldots$$ Find the balance in the account after 10 years by finding the 40th term of the sequence.Round to the nearest penny.

A)$ 7518.76
B)$ 7370.61
C)$ 7444.32
D)$ 24,005.10

Question 53

Find the indicated term of the sequence. $a _ { n } = ( - 1 ) ^ { n } ( 4 n - 2 )$ $a _ { 27 } =$ ?

A)102
B)-106
C)-110
D)6
E)-104

Question 54

Use sigma notation to write the sum. $$\frac { 1 } { 3 \cdot 2 } + \frac { 1 } { 4 \cdot 3 } + \ldots + \frac { 1 } { 8 \cdot 7 }$$

A) $$\sum _ { n = 1 } ^ { 6 } \frac { 1 } { ( n + 2 ) ! }$$
B) $\sum _ { n = 0 } ^ { 5 } \frac { 1 } { ( n + 1 ) ( n + 2 ) }$ ​
C) $$\sum _ { n = 0 } ^ { 6 } \frac { 1 } { n ( n + 1 ) }$$ ​
D) $\sum _ { n = 1 } ^ { 4 } \frac { 1 } { ( n + 1 ) ( n + 2 ) }$ ​
E) $\sum _ { n = 1 } ^ { 6 } \frac { 1 } { ( n + 1 ) ( n + 2 ) }$ ​

Question 55

​Simplify the factorial expression. $\frac { 12 ! } { 9 ! }$ ​

A)​$11880
B)​1320
C)​ $\frac { 4 } { 3 }$
D)​132
E)​$17160

Question 56

Write the first five terms of the sequence defined recursively.Use the pattern to write the nth term of the sequence as a function of n.(Assume that n begins with 1. ) $$a _ { 1 } = 19 , a _ { k + 1 } = a _ { k } - 5$$

A) $$a _ { n } = 29 - 5 n ; 19,14,9,4 , - 6$$
B) $a _ { n } = 19 ; 19,19,19,19,19$
C) $$a _ { n } = 19 ( n - 1 ) ; 14,9,4 , - 1 , - 6$$
D) $a _ { n } = 19 - 5 n ; 19,14,9,4 , - 1$
E) $a _ { n } = 24 - 5 n ; 19,14,9,4 , - 1$

Question 57

Use a calculator to find the sum.Round to four decimal places. $$\sum _ { k = 4 } ^ { 12 } \frac { - 1 } { k + 2 }$$

A)-0.9682
B)-2.2516
C)-0.0714
D)-0.8968
E)-1.7516

Question 58

Find the next term of the sequence. 64,125,216,343,...

A)524
B)4,096
C)512
D)576
E)none of these

Question 59

​Simplify the factorial expression. $$\frac { 9 ! } { 6 ! }$$

A)​5040
B)​504
C)​3024
D)​72
E)​ $\frac { 3 } { 2 }$

Question 60

Find the sum. $$\sum _ { i = 1 } ^ { 5 } - 3 i + 4$$

A)-14
B)-21
C)-25
D)-11
E)-45

Question 61

Assume that the sequence is defined recursively.Find the first three terms of the sequence.​ $$a _ { 1 } = 3 \text { and } a _ { n + 1 } = 4 a _ { n } ^ { 2 }$$ ​

A)36
B)5184
C)3
D)4
E)32

Question 62

A deposit of $ 5000 is made in an account that earns 8 % interest compounded monthly.The balance in the account after n months is given by $$A _ { n } = 5000 \left( 1 + \frac { 0.08 } { 12 } \right) ^ { n } , n = 1,2,3 , \ldots$$ Find the balance in the account after 8 years by finding the 96th term of the sequence.Round to the nearest penny.

A)$ 8,084,450.96
B)$ 9462.29
C)$ 9399.62
D)$ 483200.00
E)$ 9525.37

Question 63

Use sigma notation to write the sum. $$\frac { 1 } { 3 \cdot 2 } + \frac { 1 } { 4 \cdot 3 } + \ldots + \frac { 1 } { 8 \cdot 7 }$$

A) $\sum _ { n = 1 } ^ { 6 } \frac { 1 } { ( n + 1 ) ( n + 2 ) }$
B) $\sum _ { n = 1 } ^ { 6 } \frac { 1 } { n ( n + 1 ) }$
C) $\sum _ { n = 1 } ^ { 6 } \frac { 1 } { ( n + 2 ) ! }$
D) $\sum _ { n = 1 } ^ { 4 } \frac { 1 } { ( n + 1 ) ( n + 2 ) }$
E) $\sum _ { n = 0 } ^ { 5 } \frac { 1 } { ( n + 1 ) ( n + 2 ) }$

Question 64

Use a calculator to find the sum.Round to four decimal places. $$\sum _ { k = 3 } ^ { 9 } \frac { 3 } { k + 1 }$$

A)5.7869
B)8.7869
C)0.3
D)3.2869
E)2.9869

Question 65

Find the sum. $$\sum _ { k = 1 } ^ { 3 } \frac { 1 } { k ^ { 2 } + 4 }$$

A) $\frac { 209 } { 520 }$
B) $\frac { 1 } { 13 }$
C)1
D) $\frac { 107 } { 210 }$
E) $\frac { 12 } { 11 }$

Question 66

Find the indicated partial sum of the series. $$\sum _ { i = 1 } ^ { \infty } 2 \left( \frac { 1 } { 3 } \right) ^ { i }$$ fourth partial sum

A) $$\frac { 2 } { 81 }$$
B) $$\frac { 242 } { 81 }$$
C) $\frac { 80 } { 81 }$ ​
D) $\frac { 26 } { 81 }$ ​
E) $\frac { 82 } { 81 }$

Question 67

Evaluate the sum.​ $$\sum _ { k = 1 } ^ { 6 } 5 k$$ ​

A)105
B)97
C)30
D)28
E)210

Question 68

Evaluate the sum.​ $$\sum _ { k = 2 } ^ { 5 } 2 k$$ ​

A)28
B)5
C)2
D)56
E)none of these