Deck 8: Sequences, Series, Induction, and Probability

Question 1

An sequence is a sequence in which consecutive terms alternate in sign.

Answer 1

alternating

Question 2

The nth term of a sequence is given. Find the indicated term.
$$a _ { n } = 2 ^ { n } + 9 ; a _ { 6 }$$

A) 73
B) 576
C) 108
D) 21

Answer 2

A

Question 3

Given $\sum _ { i = 1 } ^ { n } a _ { i }$ , the variable i is called the of . The value 1 is called the
limit of summation. The value n is called the upper of summation.

Answer 3

index; summation; lower; limit

Question 4

Choose the one alternative that best completes the statement or answers the question.
The nth term of a sequence is given. Write the first four terms of the sequence.
$$a _ { n } = ( - 1 ) ^ { n } \frac { n + 3 } { n + 4 }$$

A) $\frac { 7 } { 4 } , - \frac { 11 } { 4 } , \frac { 15 } { 4 } , - \frac { 19 } { 4 }$
В) $- \frac { 4 } { 5 } , \frac { 5 } { 6 } , - \frac { 6 } { 7 } , \frac { 7 } { 8 }$
C) $- \frac { 7 } { 4 } , \frac { 11 } { 4 } , - \frac { 15 } { 4 } , \frac { 19 } { 4 }$
D) $\frac { 4 } { 5 } , - \frac { 5 } { 6 } , \frac { 6 } { 7 } , - \frac { 7 } { 8 }$

Question 5

For the expression represents the product of the first n positive integers
, For n = 0 we have 0!=

Question 6

Choose the one alternative that best completes the statement or answers the question.
The nth term of a sequence is given. Write the first four terms of the sequence.
$$a _ { n } = n \left( n ^ { 3 } - 8 \right)$$

A) $- 7,0,57,224$
B) $- 6,2,22,60$
C) $- 7 , - 4,3,16$
D) $- 6,0,4,8$

Question 7

Write the first five terms of the sequence defined recursively.
$$a _ { 1 } = 20 ; a _ { n } = \frac { 1 } { 4 } a _ { n - 1 } + 3$$

A) $a _ { 1 } = 20 , a _ { 2 } = \frac { 23 } { 4 } , a _ { 3 } = \frac { 13 } { 8 } , a _ { 4 } = \frac { 29 } { 64 } , a _ { 5 } = \frac { 1 } { 8 }$
B) $a _ { 1 } = 20 , a _ { 2 } = 23 , a _ { 3 } = 26 , a _ { 4 } = 29 , a _ { 5 } = 32$
C) $a _ { 1 } = 20 , a _ { 2 } = 5 , a _ { 3 } = \frac { 5 } { 4 } , a _ { 4 } = \frac { 5 } { 16 } , a _ { 5 } = \frac { 5 } { 64 }$
D) $a _ { 1 } = 20 , a _ { 2 } = 8 , a _ { 3 } = 5 , a _ { 4 } = \frac { 17 } { 4 } , a _ { 5 } = \frac { 65 } { 16 }$

Question 8

Write the first five terms of the sequence defined recursively.
$$b _ { 1 } = 5 ; b _ { n } = 5 b _ { n - 1 } - 3$$

A) $b _ { 1 } = 5 , b _ { 2 } = 25 , b _ { 3 } = 110 , b _ { 4 } = 535 , b _ { 5 } = 2,660$
B) $b _ { 1 } = 5 , b _ { 2 } = 10 , b _ { 3 } = 15 , b _ { 4 } = 20 , b _ { 5 } = 25$
C) $b _ { 1 } = 5 , b _ { 2 } = 22 , b _ { 3 } = 107 , b _ { 4 } = 532 , b _ { 5 } = 2,657$
D) $b _ { 1 } = 5 , b _ { 2 } = 2 , b _ { 3 } = - 1 , b _ { 4 } = - 4 , b _ { 5 } = - 7$

Question 9

Evaluate the expression.
$\frac { 9 ! } { 5 ! \cdot 4 ! }$

A) 24
B) 1
C) 126
D) 362,736

Question 10

Choose the one alternative that best completes the statement or answers the question.
The nth term of a sequence is given. Write the first four terms of the sequence.
$$a _ { n } = e ^ { 2 \ln n }$$

A) $2,4,8,16,32$
B) $e , e ^ { 2 } , e ^ { 3 } , e ^ { 4 }$
C) $1,4,9,16$
D) $2,4,6,8$

Question 11

The nth term of a sequence is given. Find the indicated term.
$$a _ { n } = \frac { 3 } { n } - 1 ; a _ { 10 }$$

A) $\frac { 1 } { 5 }$
B) $- \frac { 7 } { 10 }$
C) $\frac { 13 } { 10 }$
D) $\frac { 7 } { 10 }$

Question 12

One property of summation indicates that $$\sum _ { i = 1 } ^ { n } c =\_\_\_\_.$$

Question 13

A formula defines the nth term of a sequence as a function of one or more terms
preceding it.

Question 14

Choose the one alternative that best completes the statement or answers the question.
The nth term of a sequence is given. Write the first four terms of the sequence.
$$a _ { n } = 9 n - 7$$

A) $2,11,20,29$
B) $2,4,6,8$
C) $- 2 , - 11 , - 20 , - 29$
D) $- 2 , - 4 , - 6 , - 8$

Question 15

Choose the one alternative that best completes the statement or answers the question.
The nth term of a sequence is given. Write the first four terms of the sequence.
$$a _ { n } = \frac { ( - 1 ) ^ { n } } { n ^ { 2 } + 4 }$$

A) $\frac { 1 } { 5 } , - \frac { 1 } { 8 } , \frac { 1 } { 13 } , - \frac { 1 } { 20 }$
В) $- \frac { 1 } { 4 } , \frac { 1 } { 5 } , - \frac { 1 } { 8 } , \frac { 1 } { 13 }$
C) $- \frac { 1 } { 5 } , \frac { 1 } { 8 } , - \frac { 1 } { 13 } , \frac { 1 } { 20 }$
D) $\frac { 1 } { 4 } , - \frac { 1 } { 5 } , \frac { 1 } { 8 } , - \frac { 1 } { 13 }$

Question 16

Given an infinite sequence $\left\{ a _ { n } \right\} = a _ { 1 } , a _ { 2 } , a _ { 3 }$ , … the sum of the terms of the sequence is called an
infinite . The notation $S _ { n }$ is called the nth of the sequence and is
called a finite series.

Question 17

Choose the one alternative that best completes the statement or answers the question.
The nth term of a sequence is given. Write the first four terms of the sequence.
$$a ^ { n } = ( - 1 ) ^ { n + 1 } 3 ^ { n }$$

A) $3 , - 6,9 , - 12$
B) $- 3,6 , - 9,12$
C) $- 3,9 , - 27,81$
D) $3 , - 9,27 , - 81$

Question 18

Write the first five terms of the sequence defined recursively.
$$a _ { 1 } = 6 , a _ { n } = - \frac { 1 } { a _ { n - 1 } }$$

A) $a _ { 1 } = 6 , a _ { 2 } = \frac { 1 } { 6 } , a _ { 3 } = \frac { 1 } { 36 } , a _ { 4 } = \frac { 1 } { 216 } , a _ { 5 } = \frac { 1 } { 1,296 }$
B) $a _ { 1 } = 6 , a _ { 2 } = \frac { 1 } { 6 } , a _ { 3 } = 6 , a _ { 4 } = \frac { 1 } { 6 } , a _ { 5 } = 6$
C) $a _ { 1 } = 6 , a _ { 2 } = - \frac { 1 } { 6 } , a _ { 3 } = \frac { 1 } { 36 } , a _ { 4 } = - \frac { 1 } { 216 } , a _ { 5 } = \frac { 1 } { 1,296 }$
D) $a _ { 1 } = 6 , a _ { 2 } = - \frac { 1 } { 6 } , a _ { 3 } = 6 , a _ { 4 } = - \frac { 1 } { 6 } , a _ { 5 } = 6$

Question 19

An infinite is a function whose domain is the set of positive integers. A
sequence is a function whose domain is the set of the first n positive integers.

Question 20

The expression $a _ { n }$ is called the term or general term of a sequence.

Question 21

The nth term of a sequence is given. Find the indicated term.
$$a _ { n } = \frac { 2 ^ { n } } { ( n + 1 ) ! } ; a _ { 4 }$$

A) $\frac { 16 } { 5 }$
B) $\frac { 1 } { 15 }$
C) 2
D) $\frac { 2 } { 15 }$

Question 22

Find the sum.
$$\sum _ { n = 2 } ^ { 4 } \left( n ^ { 2 } + 5 \right)$$

A) 35
B) 50
C) 59
D) 74

Question 23

Find the sum.
$\sum _ { j = 1 } ^ { 4 } j ( j + 8 )$

A) 110
B) 36
C) 48
D) 120

Question 24

Find the sum.
$$\sum _ { i = 1 } ^ { 45 } 7$$

A) 1,035
в) 7
C) 315
D) 308

Question 25

Find the nth term $a _ { n }$ of a sequence whose first four terms are given.
$$- \frac { 6 } { 12 } , - \frac { 7 } { 24 } , - \frac { 8 } { 36 } , - \frac { 9 } { 48 } , \ldots$$

A) $a _ { n } = \frac { n - 7 } { 12 n }$
B) $a _ { n } = \frac { n + 5 } { 12 n }$
C) $a _ { n } = - \frac { n + 5 } { 12 n }$
D) $a _ { n } = \frac { 7 - n } { 12 n }$

Question 26

Evaluate the expression.
$$\frac { ( n + 2 ) ! } { ( n + 4 ) ! }$$

A) $\frac { 1 } { ( n + 4 ) ( n + 3 ) }$
B) $\frac { 1 } { ( n + 4 ) }$
C) $( n + 4 ) ( n + 3 )$
D) $\frac { 1 } { ( n + 3 ) ! }$

Question 27

Find the nth term $a _ { n }$ of a sequence whose first four terms are given.
$$\frac { 5 } { 16 } , \frac { 10 } { 25 } , \frac { 15 } { 36 } , \frac { 20 } { 49 } , \ldots$$

A) $a _ { n } = \frac { 5 ^ { n } } { ( n + 3 ) ^ { 2 } }$
B) $a _ { n } = \frac { 5 n } { ( n + 2 ) ^ { 2 } }$
C) $a _ { n } = \frac { 5 ^ { n } } { ( n + 2 ) ^ { 2 } }$
D) $a _ { n } = \frac { 5 n } { ( n + 3 ) ^ { 2 } }$

Question 28

Find the nth term $a _ { n }$ of a sequence whose first four terms are given.
$$1 , - 16,81 , - 256$$

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

Question 29

Find the sum.
$$\sum _ { k = 2 } ^ { 5 } \left( \frac { 1 } { 3 } \right) ^ { k }$$

A) $\frac { 121 } { 1024 }$
B) $\frac { 40 } { 243 }$
C) $\frac { 121 } { 243 }$
D) $\frac { 5 } { 128 }$

Question 30

Find the sum.
$$\sum _ { k = 1 } ^ { 6 } \left( - 4 k ^ { 3 } \right)$$

A) $- 1,764$
B) 540
C) $- 540$
D) 1,764

Question 31

The nth term of a sequence is given. Find the indicated term.
$$c _ { n } = \frac { ( 2 n ) ! } { 5 n } ; c _ { 5 }$$

A) 8064
B) $3,628,800$
C) 145,152
D) $\frac { 2 } { 5 }$

Question 32

Find the nth term $a _ { n }$ of a sequence whose first four terms are given.
$4,16,64,256 , \ldots$

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

Question 33

Find the sum.
$$\sum _ { j = 1 } ^ { 6 } ( - 1 ) ^ { j } ( 4 j )$$

A) $- 84$
B) 84
C) 12
D) $- 12$

Question 34

Find the sum.
$$\sum _ { j = 1 } ^ { 6 } \frac { j + 4 } { j }$$

A) $\frac { 15 } { 2 }$
B) 45
C) $\frac { 54 } { 5 }$
D) $\frac { 79 } { 5 }$

Question 35

Evaluate the expression.
$\frac { ( 6 n ) ! } { ( 6 n + 1 ) ! }$

A) $\frac { 1 } { 6 n }$
B) $\frac { 1 } { 2 }$
C) $\frac { 1 } { 6 n + 1 }$
D) $\frac { n ! } { ( n + 1 ) ! }$

Question 36

Write the sum using summation notation.
$$\frac { 1 } { 5 } + \frac { 4 } { 3 } + \frac { 27 } { 7 } + \ldots + \frac { n ^ { 3 } } { n + 4 }$$

A) $\sum _ { i = 0 } ^ { n } \frac { i ^ { 3 } } { i + 4 }$
B) $\sum _ { i = 1 } ^ { n } \frac { n ^ { 3 } } { n + 4 }$
C) $\sum _ { i = 1 } ^ { n + 1 } \frac { i ^ { 3 } } { i + 4 }$
D) $\sum _ { i = 1 } ^ { n } \frac { i ^ { 3 } } { i + 4 }$

Question 37

Find the nth term $a _ { n }$ of a sequence whose first four terms are given.
$\frac { 1 \cdot 2 \cdot 3 \cdot 4 } { 2 } , \frac { 1 \cdot 2 \cdot 3 \cdot 4 \cdot 5 } { 4 } , \frac { 1 \cdot 2 \cdot 3 \cdot 4 \cdot 5 \cdot 6 } { 6 } , \frac { 1 \cdot 2 \cdot 3 \cdot 4 \cdot 5 \cdot 6 \cdot 7 } { 8 } , \ldots$

A) $a _ { n } = \frac { ( n + 4 ) ! } { 2 ^ { n } }$
B) $a _ { n } = \frac { ( n + 4 ) ! } { 2 n }$
C) $a _ { n } = \frac { ( n + 3 ) ! } { 2 n }$
D) $a _ { n } = \frac { ( n + 3 ) ! } { 2 ^ { n } }$

Question 38

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

A) 21
B) 54
C) 27
D) 33

Question 39

Write the sum using summation notation.
$$4 + 4 + 4 + 4 + 4 + 4$$

A) $\sum _ { i = 1 } ^ { 6 } 4$
B) $\sum _ { i = 1 } ^ { 4 } 6$
C) $\sum _ { i = 1 } ^ { 6 } 4 i$
D) $\sum _ { i = 1 } ^ { n } 4$

Question 40

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

A) 130
B) 250
C) 70
D) 1,200

Question 41

Write the word or phrase that best completes each statement or answers the question.
Provide the missing information.
The difference between consecutive terms in an arithmetic sequence is called the
, and is denoted by d.

Question 42

Write the word or phrase that best completes each statement or answers the question.
Provide the missing information.
An arithmetic sequence is a linear function whose domain is the set of integers.

Question 43

Write the sum using summation notation.
$$\frac { x ^ { 2 } } { 1 } + \frac { x ^ { 4 } } { 2 } + \frac { x ^ { 6 } } { 6 } + \frac { x ^ { 8 } } { 24 } + \frac { x ^ { 10 } } { 120 }$$

A) $\sum _ { i = 1 } ^ { 5 } \frac { x ^ { 2 i } } { i ! }$
B) $\sum _ { i = 0 } ^ { 4 } \frac { x ^ { 2 i } } { i ! }$
C) $\sum _ { i = 1 } ^ { 5 } \frac { x ^ { 2 i } } { 2 ^ { i - 1 } }$
D) $\sum _ { i = 0 } ^ { 4 } \frac { x ^ { 2 i } } { ( i + 1 ) ! }$

Question 44

Choose the one alternative that best completes the statement or answers the question.
Solve the problem.
In a business meeting, every person at the meeting shakes every other person's hand exactly one time. The total number of handshakes for n people at the meeting is given by $$a _ { n } = \frac { 1 } { 2 } n ( n - 1 )$$ Evaluate $a _ { 12 }$ and interpret its meaning in the context of this problem.

A) 132; If 12 people are present at the meeting there will be 132 handshakes.
B) 66; If 12 people are present at the meeting there will be 66 handshakes.
C) 11; The 12th person shakes performs 11 handshakes.
D) 78; If 12 people are present at the meeting there will be 78 handshakes.

Question 45

Write the word or phrase that best completes each statement or answers the question.
Provide the missing information.
An sequence is a sequence in which each term after the first differs from its predecessor
by a fixed constant.

Question 46

Choose the one alternative that best completes the statement or answers the question.
Determine whether the sequence is arithmetic. If so, find the common difference.
4, -16, 64, -256, . . .

A) not arithmetic
B) arithmetic; d = -4
C) arithmetic; d = 4
D) arithmetic; d = -2

Question 47

Write the word or phrase that best completes each statement or answers the question.
Provide the missing information.
Given an arithmetic sequence with first term $a _ { 1 }$ , and common difference d, the nth term is
represented by the formula $a _ { \mathrm { n } } =$ .

Question 48

Write the first four terms of an arithmetic sequence, $\left\{ a _ { n } \right\}$ , based on the given information about the
sequence.
$$a _ { 1 } = 3 , d = 6$$

A) $18,108,648,3,888$
B) $3,9,15,21$
C) $3,18,108,648$
D) $9,15,21,27$

Question 49

Write the sum using summation notation.
$$\frac { 1 } { x + 3 } + \frac { 2 } { x + 6 } + \frac { 6 } { x + 9 } + \frac { 24 } { x + 12 } + \frac { 120 } { x + 15 }$$

A) $\sum _ { i = 1 } ^ { 5 } \frac { i ! } { x + 3 i }$
В) $\sum _ { i = 1 } ^ { 5 } \frac { i ! } { x + i }$
C) $\sum _ { i = 1 } ^ { 5 } \frac { 2 ^ { i - 1 } } { x + 3 i }$
D) $\sum _ { i = 1 } ^ { 5 } \frac { i ! } { x + 3 }$

Question 50

Choose the one alternative that best completes the statement or answers the question.
Determine whether the sequence is arithmetic. If so, find the common difference.
$5 , \frac { 25 } { 6 } , \frac { 125 } { 36 } , \frac { 625 } { 216 }$

A) arithmetic; $d = 5$
B) not arithmetic
C) arithmetic; $d = \frac { 5 } { 6 }$
D) arithmetic; $d = \frac { 6 } { 5 }$

Question 51

Write the word or phrase that best completes each statement or answers the question.
Provide the missing information.
Given an arithmetic sequence with first term a1 and nth term an, the nth partial sum is given by the
formula

Question 52

Write the sum using summation notation.
$$- \frac { 1 } { 3 } + \frac { 1 } { 9 } - \frac { 1 } { 27 } + \frac { 1 } { 81 } - \frac { 1 } { 243 }$$

A) $\sum _ { i = 1 } ^ { 5 } \left( ( - 1 ) ^ { i + 1 } \frac { 1 } { 3 i } \right)$
B) $\sum _ { i = 1 } ^ { 5 } \left( ( - 1 ) ^ { i } \frac { 1 } { 3 i } \right)$
C) $\sum _ { i = 1 } ^ { 5 } \left( ( - 1 ) ^ { i } \frac { 1 } { 3 ^ { i } } \right)$
D) $\sum _ { i = 1 } ^ { 5 } \left( ( - 1 ) ^ { i + 1 } \frac { 1 } { 3 ^ { i } } \right)$

Question 53

Write the first four terms of the arithmetic sequence with the given first term and common difference.
$$a _ { 1 } = 9 , d = - 7$$

A) $9,16,23,30$
В) $9,2 , - 5 , - 12$
C) $- 7 , - 16 , - 25 , - 34$
D) $- 7,2,11,20$

Question 54

Solve the problem.
Expenses for a company for year 1 are $\$ 20,000$ . Every year thereafter, expenses increase by $\$ 1,500$ plus $2 \%$ of the cost of the prior year. Let $a _ { 1 }$ represent the original cost for year 1 ; that is $a _ { 1 } = 20,000$ .
Use a recursive formula to find the cost $a _ { n }$ in terms of $a _ { n - 1 }$ for each subsequent year, $\mathrm { n } \geq 2$ .

A) $a _ { n } = 1.02 a _ { n - 1 } + 21,500 , n \geq 2$
B) $a _ { n } = 0.02 a _ { n - 1 } + 1,500 , n \geq 2$
C) $a _ { n } = 1.02 a _ { n - 1 } + 1,500 , n \geq 2$
D) $a _ { n } = 0.02 a _ { n - 1 } + 21,500 , n \geq 2$

Question 55

Write the sum using summation notation.
$$- 3 + 9 - 27 + 81$$

A) $\sum _ { n = 1 } ^ { 4 } ( - 1 ) ^ { n _ { 3 } n }$
B)
C) $\sum _ { n = 1 } ^ { 4 } ( - 1 ) ^ { n + 1 } n$
D) $\sum _ { n = 1 } ^ { 4 } ( - 1 ) ^ { n _ { n } }$

Question 56

Write the word or phrase that best completes each statement or answers the question.
Provide the missing information.
The sum of the first n terms of a sequence is called the nth sum and is denoted by $S _ { n }$

Question 57

Rewrite the series as an equivalent series with the new index of summation.
$$\sum _ { i = 1 } ^ { 7 } ( 9 i ) = \sum _ { k = 3 } ^ { ? } ( ? )$$

A) $\sum _ { k = 3 } ^ { 9 } [ 9 ( k - 2 ) ]$
B) $\sum _ { k = 3 } ^ { 9 } [ 9 ( k + 2 ) ]$
C) $\sum _ { k = 3 } ^ { 9 } [ 9 ( k - 3 ) ]$
D) $\sum _ { k = 3 } ^ { 9 } [ 9 ( k + 3 ) ]$

Question 58

Write the sum using summation notation.
$$a + a r + a r ^ { 2 } + a r ^ { 3 } + \ldots + a r ^ { 19 }$$

A) $\sum _ { i = 1 } ^ { 19 } a r ^ { j - 1 }$
B) $\sum _ { i = 1 } ^ { 20 } a r ^ { i - 1 }$
C) $\sum _ { i = 1 } ^ { 19 } a r ^ { i }$
D) $\sum _ { i = 1 } ^ { 20 } a r ^ { i }$

Question 59

Use the provided sums to evaluate the given expression.
$\sum _ { i = 1 } ^ { 40 } i = 820$ and $\sum _ { i = 1 } ^ { 40 } i ^ { 2 } = 22,140 ;$ evaluate $\sum _ { i = 1 } ^ { 40 } \left( 5 i ^ { 2 } + 9 i \right)$

A) 118,080
B) 22,960
C) 111,520
D) 203,360

Question 60

Write the first four terms of an arithmetic sequence, $\left\{ a _ { n } \right\}$ , based on the given information about the
sequence.
Write the first five terms of the arithmetic sequence. $$a _ { 1 } = 3 , d = - 4$$

A) $- 4 , - 1,5,23,77$
B) $- 4 , - 1,2,5,8$
C) $3 , - 1,19 , - 61,259$
D) $3 , - 1 , - 5 , - 9 , - 13$

Question 61

Solve the problem.
A student studying to be a veterinarian's assistant keeps track of a kitten's weight each week for a 5-week period after birth. $$\begin{array}{l}\text { Week number } 1 \quad 2 \quad 3 \quad 4 \quad 5\\\begin{array} { l l l l l l } \text { Weight (lb) } & 0.7 & 0.97 & 1.24 & 1.51 & 1.78\end{array}\end{array}$$ a. Write an expression for the nth term of the sequence representing the kitten's weight, n weeks after birth.
B) If the weight of the kitten continues to increase linearly for 3 months, predict the kitten's weight 10 weeks
After birth. A) a. $a _ { n } = 0.27 n + 0.43$
b. $2.7 \mathrm { lb }$
B) a. $a _ { n } = 0.27 n + 0.7$
b. $2.7 \mathrm { lb }$

C) a. $a _ { n } = 0.27 n + 0.43$
b. $3.13 \mathrm { lb }$

D) a. $a _ { n } = 0.27 n + 0.7$
b. $3.4 \mathrm { lb }$

Question 62

Find the indicated term of the arithmetic sequence based on the given information.
$a _ { 1 } = \frac { 4 } { 5 } , d = \frac { 1 } { 3 } ;$ Find $a _ { 24 }$

A) $\frac { 142 } { 15 }$
B) $\frac { 127 } { 15 }$
C) $\frac { 44 } { 5 }$
D) $\frac { 137 } { 15 }$

Question 63

Write a nonrecursive formula for the nth term of the arithmetic sequence {an} based on the given
information.
$$a _ { 1 } = \frac { 1 } { 2 } , d = \frac { 2 } { 3 }$$

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

Question 64

Find the number of terms of the finite arithmetic sequence.
$12,11.7,11.4,11.1 , \ldots , - 2.4$

A) 48
В) 50
C) 51
D) 49

Question 65

Find the indicated term of the arithmetic sequence based on the given information.
$a _ { 17 } = 9.76$ and $a _ { 41 } = 10.72 ;$ Find $a _ { 108 }$

A) $13.48$
B) $13.44$
C) $13.4$
D) $- 4.76$

Question 66

Find the indicated term.
$a _ { 1 } = \frac { 1 } { 2 } , d = \frac { 1 } { 5 } ;$ Find $a _ { 11 }$

A) $\frac { 27 } { 10 }$
B) $\frac { 29 } { 10 }$
C) $\frac { 19 } { 10 }$
D) $\frac { 5 } { 2 }$

Question 67

Write a recursive formula to define the sequence.
$$a _ { 1 } = 2 , d = - 9$$

A) $a _ { 1 } = 2$ and $a _ { n } = a _ { n - 1 } + 9$ for $n \geq 2$
B) $a _ { 1 } = 2$ and $a _ { n } = a _ { n - 1 } - 9$ for $n \geq 2$
C) $a _ { 1 } = 2$ and $a _ { n } = a _ { n + 1 } - 9$ for $n \geq 2$
D) $a _ { 1 } = 2$ and $a _ { n } = - 9 a _ { n - 1 }$ for $n \geq 2$

Question 68

Find the indicated term of the arithmetic sequence based on the given information.
$a _ { 15 } = 67$ and $a _ { 41 } = 223 ;$ Find $a _ { 108 }$

A) 631
B) 671
C) 625
D) 637

Question 69

Find the indicated term of the arithmetic sequence based on the given information.
$a _ { 1 } = 36$ and $a _ { 6 } = 11 ;$ Find $a _ { 33 }$ .

A) $- 129$
B) $- 119$
C) $- 114$
D) $- 124$

Question 70

Solve the problem.
A physical activity class requires students to jog around an indoor track. For the first week of class the students jog 300 m around the track each day. Each week thereafter, the students increase the
Distance jogged by 125 m. Write the nth term of a sequence defining the number of meters jogged
Each day by the students in the nth week of class. A) $a _ { n } = 125 n + 175$
В) $a _ { n } = 125 n + 300$
C) $a _ { n } = 175 n + 125$
D) $a _ { n } = 300 n + 125$

Question 71

Write a recursive formula to define the sequence.
$$a _ { 1 } = 5 , d = 4$$

A) $a _ { 1 } = 5$ and $a _ { n } = a _ { n - 1 } - 4$ for $n \geq 2$
B) $a _ { 1 } = 5$ and $a _ { n } = a _ { n + 1 } + 4$ for $n \geq 2$
C) $a _ { 1 } = 5$ and $a _ { n } = a _ { n - 1 } + 4$ for $n \geq 2$
D) $a _ { 1 } = 5$ and $a _ { n } = 4 a _ { n - 1 }$ for $n \geq 2$

Question 72

Write a nonrecursive formula for the nth term of the arithmetic sequence {an} based on the given
information.
$$a _ { 1 } = 6 , d = 4$$

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

Question 73

Find the number of terms of the finite arithmetic sequence.
$12,21,30,39 , \ldots , 525$

A) 58
B) 59
C) 60
D) 57

Question 74

Find the sum.
Find the sum of the first 36 terms of the sequence. $\{ 1,8,15,22,29 , \ldots \}$

A) 4,572
B) 9,144
C) 4,446
D) 9,108

Question 75

From the given terms of the arithmetic sequence, find a1 and d.
$a _ { 12 } = 50$ and $a _ { 25 } = 89$

A) $a _ { 1 } = 17 , d = 3$
B) $a _ { 1 } = 20 , d = 3$
C) $a _ { 1 } = 2 , d = 4$
D) $a _ { 1 } = 14 , d = 3$

Question 76

Find the indicated term of the arithmetic sequence based on the given information.
$a _ { 1 } = - 11$ and $a _ { 16 } = 19 ;$ Find $a _ { 13 }$

A) 13
B) 19
C) 25
D) 15

Question 77

Find the indicated term of the arithmetic sequence based on the given information.
$a _ { 1 } = 38 , d = 3$ ; Find $a _ { 25 }$ .

A) 113
B) 104
C) 110
D) 107

Question 78

Find the sum.
$$3 + 4.6 + 6.2 + 7.8 + \ldots + 55.8$$

A) $999.6$
В) $77.4$
C) $1,002.8$
D) 387

Question 79

Find the indicated term of the arithmetic sequence based on the given information.
$a _ { 1 } = 13$ and $a _ { 18 } = - 55 ;$ Find $a _ { 9 }$

A) $- 91$
В) $- 19$
C) $- 55$
D) $- 23$

Question 80

Find the indicated term.
$a _ { 1 } = - 11 , d = 9 ;$ Find $a _ { 18 }$

A) 133
B) 182
C) $- 351$
D) 142