Deck 11: Miscellaneous Topics

Question 1

Find the 37th term of the arithmetic sequence with a = 8 and d = 12.

A) 423
B) 440
C) 411
D) 495

Answer 1

440

Question 2

Use the binomial theorem to expand the expression. ( - ) ⁴

A)
B)
C)
D)

Answer 2

Question 3

Expand: ( + ) ²

A)
B)
C)
D)

Answer 3

Question 4

Use the binomial theorem to expand the expression. ( + ) ⁴

A)
B)
C)
D)

Question 5

Given an infinite sequence with a _n = 4 n + 8, find a ₃₁.

A) a ₃₁ = 132
B) a ₃₁ = 156
C) a ₃₁ = 63
D) a ₃₁ = 116

Question 6

Find the term in the expansion of .

A)
B)
C)
D)

Question 7

Find the term in the expansion of .

A)
B)
C)
D)

Question 8

Evaluate the expression.

A)
B)
C)
D)

Question 9

Find the 50th term of the arithmetic sequence with a = - 8 and d = 4.

A) 146
B) 202
C) 188
D) 159

Question 10

Find the term in the expansion of .

A)
B)
C)
D)

Question 11

Use the binomial theorem to expand the expression. ( + ) ³

A)
B)
C)
D)

Question 12

Use the binomial theorem to expand the expression. ( x + 3 y ) ³

A)
B)
C)
D)

Question 13

Evaluate the expression

A)
B)
C)
D)

Question 14

Expand: ( - ) ³

A)
B)
C)
D)

Question 15

Given an infinite sequence with a _n = 2 n , find a ₄₅.

A) a ₄₅ = 92
B) a ₄₅ = 88
C) a ₄₅ = 47
D) a ₄₅ = 90

Question 16

Evaluate the expression

A)
B)
C)
D)

Question 17

Use the binomial theorem to expand the expression. ( 7 x - 6 y ) ³

A)
B)
C)
D)

Question 18

Use the binomial theorem to expand the expression. ( 3 x + 4 y ) ³

A)
B)
C)
D)

Question 19

Given an infinite sequence with find a ₃₆.

A) a ₃₆ = 129
B) a ₃₆ = 101
C) a ₃₆ = 57
D) a ₃₆ = 115

Question 20

Expand: ( - ) ⁴

A)
B)
C)
D)

Question 21

The first three terms of an arithmetic sequence are 1, 5, 9, find the 10th term.

A) 13
B) 35
C) 41
D) 37

Question 22

Show that

A)
B)

Question 23

Find the sum of the first n terms of the following arithmetic sequence: 8, 17, 26, ... ; n = 25

A) 2,900
B) 2,988
C) 2,854
D) 2,839

Question 24

Find the tenth term of the geometric sequence with a = 5 and r = 2.

A) tenth term = 2,560
B) tenth term = 5,120
C) tenth term = 2,552
D) tenth term = 2,558

Question 25

The first three terms of an arithmetic sequence are 23, 22, 21, find the 86th term.

A) -62
B) -108
C) 1,954
D) -63

Question 26

Write the first three terms of the geometric sequence with a = 3 and r = 3.

A) 3, 9, 27
B) 3, 6, 9
C) 3 , 9, 27

Question 27

The first three terms of an arithmetic sequence are -318, -306, -294, find the 119th term.

A) 1,734
B) 1,098
C) -37,512
D) 1,110

Question 28

Find the sum.

A) 152
B) 159
C) 123
D) 110

Question 29

Write the first four terms of the geometric sequence with a = 12 and a third term of 108.

A) 12, 36, 108, 324
B) 13, 41, 109, 324
C) 12, 37, 109, 323
D) 7, 10, 13, 16

Question 30

Find the sum of the first n terms of the following arithmetic sequence: Second term is 13, third term is 21; n = 17

A) 1,219
B) 1,173
C) 1,085
D) 1,112

Question 31

Find the sum of the first 60 even natural numbers.

A) 3,748
B) 3,599
C) 3,706
D) 3,660

Question 32

Write the first five terms of the geometric sequence with a = 5 and a fourth term of 135.

A) 5, 15, 45, 135, 405
B) 5, 16, 41, 138, 405
C) 5, 15, 46, 138, 402
D) 5, 8, 11, 14, 17

Question 33

Find the first term of the arithmetic sequence with a common difference of 5 and whose 59th term is 281.

A) 4
B) 13
C) - 9
D) - 7

Question 34

Find the negative geometric mean between 3 and 21.

A)
B)
C)
D)

Question 35

What is the arithmetic mean between 6 and 28?

A) 22
B) 17
C) 28
D) 6
E) 11

Question 36

Insert two arithmetic means between 11 and 26.

A) 15, 22
B) 17, 21
C) 16, 21
D) 16, 20

Question 37

Find the sum.

A) 178
B) 166
C) 189
D) 195

Question 38

Insert four arithmetic means between 18 and 43.

A) 23, 27, 33, 40
B) 23, 28, 33, 38
C) 23, 28, 32, 37
D) 22, 28, 33, 39

Question 39

Write the first five terms of the geometric sequence with a = - 2 and a fourth term of -54.

A) -2, -3, -21, -51, -165
B) -2, -6, -18, -54, -162
C) -2, -5, -8, -11, -14
D) -2, 3, -16, 51, -162

Question 40

Write the first five terms of the geometric sequence with a = - 3 and r = 4.

A) -3, 12, -48, 192, -768
B) -3, -7, -11, -15, -19
C) -3, -12, -48, -192, -768

Question 41

Find the sum of each infinite geometric sequence.

A) S = 40
B) S = 20
C) S = 35
D) S = 30

Question 42

A house appreciates by 6% each year. If the house is worth $77,000 today, how much will it be worth 15 years from now? Round your answer to the nearest cent.

A) $184,541.99
B) $184,543.99
C) $184,534.98
D) $184,520.98

Question 43

The third partial sum of the sequence 3, 9, 27, 81, ... is __________.

A)
B)
C) 3 + 9 + 27 = 39
D) 3 + 9 + 27 + 81 = 120

Question 44

Change the decimal to a common fraction. Then check your answer by doing a long division.

A)
B)
C)
D)

Question 45

Find the sum of the first 8 terms of the geometric sequence 4, -20, 100, ...

Question 46

Find the sum of the infinite geometric sequence.

A)
B)
C)
D)

Question 47

Find the sum of the first 5 terms of the geometric sequence 2, -4, 8, ...

Question 48

The fourth partial sum of the sequence 6, 3, 1.5, 0.75, ... is __________.

A)
B)
C) 0.75
D) 6 + 3 + 1.5 + 0.75 = 11.25

Question 49

Find the sum of the infinite geometric sequence.

A) S = 24
B) S = 48
C) S = 36
D) S = 32

Question 50

Change the decimal to a common fraction. Then check your answer by doing a long division.

A)
B)
C)
D)

Question 51

Change the decimal to a common fraction. Then check your answer by doing long division.

A)
B)
C)
D)

Question 52

Use the formula for the sum of a geometric sequence to solve the problem. After a sales clerk works six months, her employer will begin an annuity for her and will contribute $550 every six months to a fund that pays 6% annual interest. After she has been employed for three years, what will be the amount of the annuity? Round your answer to the nearest cent.

A) $3,554.62
B) $3,565.25
C) $3,557.63
D) $3,487.63

Question 53

Insert four geometric means between 4 and 128.

A) 9, 15, 33, 63
B) 10, 14, 34, 62
C) 8, 16, 32, 64
D) 8, 15, 33, 64

Question 54

Find the sum of the infinite geometric sequence, if possible.

A)
B)
C)
D) No sum

Question 55

Insert three geometric means ( two positive and one negative ) between - 84 and - 6,804.

A) 250, - 754, 754
B) 252, - 755, 754
C) 252, - 756, 2,268
D) 253, 755, - 2,267

Question 56

Paula has five ways to travel from New York to Chicago, three ways to travel from Chicago to Denver, and six ways to travel from Denver to Los Angeles. How many choices are available to Paula if she travels from New York to Los Angeles?

A) 97
B) 92
C) 105
D) 90

Question 57

The population of Bensville is decreasing by 10% each year. If its current population is 96, what will be the approximate population 6 years from now?

A) 51
B) 45
C) 37
D) 56

Question 58

Find the sum of the first 8 terms of the geometric sequence 2, -8, 32, ...

Question 59

Find the sum of the infinite geometric sequence.

A) S = 40
B) S = 20
C) S = 35
D) S = 30

Question 60

Find the sum of the infinite geometric sequence, if possible.

A)
B)
C)
D) No sum

Question 61

Which of the following is the sample set for an experiment which involves tossing three coins?

A) HHH, TTT
B) HHH, HHT, HTT, TTT
C) HHH, HHT, HTH, THH, TTT
D) HHH, HHT, HTH, THH, TTH, THT, HTT, TTT

Question 62

An ordinary die is rolled once. What is the probability of rolling an odd number?

A)
B)
C)
D)

Question 63

Robert plans to go to dinner and see a movie. In how many ways can he arrange her evening if he has a choice of 4 movies and 3 restaurants?

A) 12
B) 7
C) 1
D) 4

Question 64

How many seven-digit phone numbers are available in area code 837 if no phone number can begin with 0 and 1?

A) 1,000,000
B) 8,000,000
C) 4,500,000

Question 65

Find the term in the expansion of .

A)
B)
C)
D)

Question 66

How many four-digit license plates can be manufactured? Note that there are ten choices - 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 - for each digit.

A) 100,000
B) 72,000
C) 10,000
D) 30,000

Question 67

Find the term in the expansion of .

A)
B)
C)
D)

Question 68

Jeff must read 4 books from a reading list of 13. How many choices does he have?

A) 715
B) 716
C) 721
D) 703

Question 69

Balls numbered from 1 to 38 are placed in a container and stirred. If one is drawn at random, what is the probability that the number is a prime number?

A)
B)
C)
D)

Question 70

Find a sample space for an experiment of rolling a dice and picking a card suit.

A) {(0, ♠), (1, ♠), (2, ♠), (3, ♠), (4, ♠), (5, ♠), (0, ♣), (1, ♣), (2, ♣), (3, ♣), (4, ♣), (5, ♣), (0, ♥), (1, ♥), (2, ♥), (3, ♥), (4, ♥), (5, ♥), (0, ♦), (1, ♦), (2, ♦), (3, ♦), (4, ♦), (5, ♦)}
B) {(1, ♠), (2, ♠), (3, ♠), (4, ♠), (5, ♠), (6, ♠) (1, ♣), (2, ♣), (3, ♣), (4, ♣), (5, ♣), (6, ♣) (1, ♥), (2, ♥), (3, ♥), (4, ♥), (5, ♥), (6, ♥) (1, ♦), (2, ♦), (3, ♦), (4, ♦), (5, ♦), (6, ♦)}
C) {(1, ♠), (2, ♠), (3, ♠), (4, ♠), (1, ♣), (2, ♣), (3, ♣), (4, ♣), (1, ♥), (2, ♥), (3, ♥), (4, ♥), (1, ♦), (2, ♦), (3, ♦), (4, ♦)}
D) {(1, ♠), (2, ♣), (3, ♥), (4, ♦)}

Question 71

In one state lottery, anyone who picks the correct 5 numbers (in any order) wins. With the numbers 0 through 49 available, how many choices are possible?

A) 2,119,260
B) 2,118,752
C) 2,118,762
D) 2,118,760

Question 72

In how many ways can 8 plates be placed on a table?

A) 8
B) 64
C) 40,320
D) 256

Question 73

In how many ways can we select a committee of three men and three women from a group composed of four men and five women?

A) 40
B) 35
C) 21
D) 33

Question 74

Find a sample space for an experiment of rolling a dice.

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

Question 75

Refer to the following spinner. If the spinner is spun, what is the probability that the arrow will stop on green? Assume that the spinner never stops on a line.

A)
B)
C)
D)

Question 76

Find the term in the expansion of .

A)
B)
C)
D)

Question 77

How many permutations does a combination lock have if each combination has three numbers, no two numbers of any combination are equal, and the lock has 25 numbers?

A) 13,806
B) 13,757
C) 13,797
D) 13,800