Deck 11: Sequences, Series, and Probability

Question 1

Find the first five terms of the infinite sequence whose nth term is given.

A) 0, 2, 6, 12, 20
B) 0, 3, 8, 15, 24
C) 1, 4, 9, 16, 25
D) 2, 6, 12, 20, 30

Answer 1

0, 2, 6, 12, 20

Question 2

Find the first five terms of the infinite sequence whose nth term is given.

A)
B)
C)
D)

Answer 2

Question 3

Find all the terms of the finite sequence.

A) 1, -1, 1, -1, 1
B) 1, 1, 1, 1, 1
C) -1, 1, -1, 1, -1
D) -1,-1,-1,-1,-1

Answer 3

1, -1, 1, -1, 1

Question 4

Write a formula for the nth term of the infinite sequence. Do not use a recursion formula.

A)
B)
C)
D)

Question 5

Write a formula for the nth term of the infinite sequence. Do not use a recursion formula.
2, 4, 8, 16, 32, . . .

A)
B)
C)
D)

Question 6

Write a formula for the nth term of the infinite sequence. Do not use a recursion formula.

A)
B)
C)
D)

Question 7

Write a formula for the nth term of the infinite sequence. Do not use a recursion formula.

A)
B)
C)
D)

Question 8

Write a formula for the nth term of the infinite sequence. Do not use a recursion formula.
2 , 8 , 14 , 20 , 26 , . . .

A)
B)
C)
D)

Question 9

Find the first five terms of the infinite sequence whose nth term is given.

A)
B)
C)
D)

Question 10

Find all the terms of the finite sequence.

A) 4, 16, 64, 256, 1024
B) 1, 4, 16, 64, 256
C) 1, 16, 81, 256, 625
D) 16, 64, 256, 1024, 4096

Question 11

Find all the terms of the finite sequence.

A) -1, 0, 1, 2, 3
B) -1, 1, 3, 5, 7
C) 1, -1, -3, -5, -7
D) 5, 7, 9, 11, 13

Question 12

Find all the terms of the finite sequence.

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

Question 13

Find all the terms of the finite sequence.

A) 2, 6, 12, 20, 30
B) 1, 4, 9, 16, 25
C) 0, 2, 6, 12, 20
D) 0, 3, 8, 15, 24

Question 14

Find the first five terms of the infinite sequence whose nth term is given.

A) 0, -2, -4, -6, -8
B) 0, 1, 2, 3, 4
C) 0, 2, 4, 6, 8
D) 4, 6, 8, 10, 12

Question 15

Find the first five terms of the infinite sequence whose nth term is given.

A) 2, 10, 18, 26, 34
B) -6, 2, 10, 18, 26
C) 2, 4, 6, 8, 10
D) 1, 5, 9, 13, 17

Question 16

Find the first five terms of the infinite sequence whose nth term is given.

A) 2, 4, 8, 16, 32
B) 1, 2, 4, 8, 16
C) 4, 8, 16, 32, 64
D) 1, 4, 9, 16, 25

Question 17

Find the first five terms of the infinite sequence whose nth term is given.

A)
B)
C)
D)

Question 18

Find all the terms of the finite sequence.

A)
B)
C)
D)

Question 19

Find the first five terms of the infinite sequence whose nth term is given.

A)
B)
C)
D)

Question 20

Find the first five terms of the infinite sequence whose nth term is given.

A) -8, -6, -4, -2, 0
B) -3, -2, -1, 0, 1
C) -2, -1, 0, 1, 2
D) -1, 0, 1, 2, 3

Question 21

Determine if the given sequence could be an arithmetic sequence.
2, 8, 32, 128, 512, . . .

A) Yes
B) No

Question 22

Determine if the given sequence could be an arithmetic sequence.
2, 5, 8, 11, 14, . . .

A) Yes
B) No

Question 23

Write a formula for the nth term of the arithmetic sequence. Do not use a recursion formula.
-5, -2, 1, 4, 7, . . .

A)
B)
C)
D)

Question 24

Find the first five terms of the arithmetic sequence.

A) 8, 20, 32, 44, 56
B) -4, 8, 20, 32, 44
C) 2, 5, 8, 11, 14
D) 8, 16, 24, 32, 40

Question 25

Write a formula for the nth term of the arithmetic sequence. Do not use a recursion formula.
-3, 3, 9, 15, 21, . . .

A)
B)
C)
D)

Question 26

Determine if the given sequence could be an arithmetic sequence.
1, -3, 9, -27, 81, . . .

A) Yes
B) No

Question 27

Determine if the given sequence could be an arithmetic sequence.
-5 , -9 , -13 , -17 , . . .

A) Yes
B) No

Question 28

Find the first six terms of the sequence.

A) 0, 3, -18, -15, -12, -9
B) -6, -18, -15, -12, -9, -6
C) -6, -12, -24, -48, -96, -192
D) -12, -24, -48, -96, -192, -384

Question 29

Determine if the given sequence could be an arithmetic sequence.

A) Yes
B) No

Question 30

Determine if the given sequence could be an arithmetic sequence.

A) Yes
B) No

Question 31

Write a formula for the nth term of the arithmetic sequence. Do not use a recursion formula.
4, 6, 8, 10, 12, . . .

A)
B)
C)
D)

Question 32

Find the first five terms of the arithmetic sequence.

A) -6, -5, -4, -3, -2
B) -24, -18, -12, -6, 0
C) -5, -4, -3, -2, -1
D) 1, 2, 3, 4, 5

Question 33

Write a formula for the nth term of the arithmetic sequence. Do not use a recursion formula.
0.23, 0.26, 0.29, 0.32, 0.35, . . .

A)
B)
C)
D)

Question 34

Find the first six terms of the sequence.

A) 7, 9, 11, 13, 15, 17
B) 0, 2, 4, 6, 8, 10
C) 5, 2, 4, 6, 8, 10
D) 5, 7, 9, 11, 13, 15

Question 35

Find the first six terms of the sequence.

A) -1, -4, 1, -4, -1, -4
B) -1, 2, 1, 2, 1, 2
C) -1, 4, -1, 4, -1, 4
D) -1, 2, -1, 2, -1, 2

Question 36

Find the first five terms of the arithmetic sequence.

A) -2, -5, -8, -11, -14
B) 2, 5, 8, 11, 14
C) 4, 7, 10, 13, 16
D) 2, 3, 4, 5, 6

Question 37

Find the first six terms of the sequence.

A)
B)
C)
D)

Question 38

Write a formula for the nth term of the arithmetic sequence. Do not use a recursion formula.
-2, -8, -14, -20, -26, . . .

A)
B)
C)
D)

Question 39

Write a formula for the nth term of the infinite sequence. Do not use a recursion formula.

A)
B)
C)
D)

Question 40

Find the indicated part of the arithmetic sequence.
Find the eighth term of the sequence that has a first term of -8 and a common difference of 5.

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

Question 41

Solve the problem.
A town has a population of 3000 people and is increasing by 9% every year. What will the population be at the end of 8 years? Round answer to the nearest whole number.

A) 5160
B) 5978
C) 6516
D) 5484

Question 42

Find the indicated part of the arithmetic sequence.
Find the common difference of the sequence in which the first term is -10 and the 8th term is -31.

A)
B)
C) 3
D) -3

Question 43

Write a recursion formula for the sequence.
7, 35, 175, 875, . . .

A)
B)
C)
D)

Question 44

Find the indicated part of the arithmetic sequence.
Find the 34th term of the sequence that has a first term of 7 and a common difference of -5.

A) -158
B) 172
C) -163
D) 177

Question 45

Write a recursion formula for the sequence.
-8, -1, 6, 13, . . .

A)
B)
C)
D)

Question 46

Write a recursion formula for the sequence.

A)
B)
C)
D)

Question 47

Write a recursion formula for the sequence.
3, -9, 27, -81, . . .

A)
B)
C)
D)

Question 48

Find the indicated part of the arithmetic sequence.
Find term 49 of the sequence that has a first term of -8 and a common difference of

A) 28
B)
C) - 44
D)

Question 49

Find the indicated part of the arithmetic sequence.
Find the common difference of the sequence in which the first term is 15 and the 26th term is 165.

A) - 7513
B) -6
C) 7513
D) 6

Question 50

Write a recursion formula for the sequence.
-3, 7, 17, 27, . . .

A)
B)
C)
D)

Question 51

Find the indicated part of the arithmetic sequence.
Find the common difference of the sequence in which the first term is 8 and the 106th term is 15.

A) -7
B) 7
C)
D)

Question 52

Solve the problem.
The population of a town was 34,200 at the beginning of 1970. If the population decreased by 350 people per year, how many people lived in the town at the beginning of 1985?

A) 28,950
B) 28,600
C) 5250
D) 29,300

Question 53

Solve the problem.
A man earned $3000 the first year he worked. If he received a raise of $600 at the end of each year, what was his salary during the 15th year?

A) $11,400
B) $8400
C) None of these
D) $12,000

Question 54

Find the indicated part of the arithmetic sequence.
Find a formula for given that

A)
B)
C)
D)

Question 55

Write a recursion formula for the sequence.

A)
B)
C)
D)

Question 56

Write a recursion formula for the sequence.
7, 16, 25, 34, . . .

A)
B)
C)
D)

Question 57

Find the indicated part of the arithmetic sequence.
Find the 17th term of the sequence that has a first term of 5 and a common difference of

A) 1
B)
C)
D) 9

Question 58

Find the sum of the series.

A) 8
B) 30
C) 14
D) 22

Question 59

Find the sum of the series.

A) 64
B) 66
C) 54
D) 34

Question 60

Solve the problem.
A town has a population of 20,000 people and is increasing by 10% every year. What will the population be at the end of 6 years? Round answer to the nearest whole number.

A) 32,000
B) 32,210
C) 35,431
D) 15,431

Question 61

Find the sum of the series.

A) 7
B) 9
C) 14
D) 5

Question 62

Rewrite the series using the new index j as indicated.

A)
B)
C)
D)

Question 63

Find the sum of the series.

A) 30,558
B) 174
C) -174
D) 26

Question 64

Write the series in summation notation. Use the index i and let i begin at 1 in each summation.
0 + 2 + 6 + 12 + 20

A)
B)
C)
D)

Question 65

Rewrite the series using the new index j as indicated.

A)
B)
C)
D)

Question 66

Write the series in summation notation. Use the index i and let i begin at 1 in each summation.
4 + 7 + 10 + 13 + 16

A)
B)
C)
D)

Question 67

Find the sum of the series.

A) 262,144
B) 5440
C) 384
D) 4096

Question 68

Write the series in summation notation. Use the index i and let i begin at 1 in each summation.
6 + 10 + 14 + 18 + 22

A)
B)
C)
D)

Question 69

Write the series in summation notation. Use the index i and let i begin at 1 in each summation.

A)
B)
C)
D)

Question 70

Find the sum of the series.

A) 10
B) 34
C) 24
D) 33

Question 71

Find the sum of the series.

A) 7
B) 4
C) 16
D) 14

Question 72

Determine whether the equation is true or false.

Question 73

Write out all the terms of the series.

A)
B) 6x + 7x + 8x + 9x + . . .
C) 7x + 8x + 9x + 10x
D) 6x + 7x + 8x + 9x

Question 74

Write the series in summation notation. Use the index i and let i begin at 1 in each summation.
-1 + 0 + 1 + 2 + 3

A)
B)
C)
D)

Question 75

Write the series in summation notation. Use the index i and let i begin at 1 in each summation.

A)
B)
C)
D)

Question 76

Find the sum of the series.

A) 6561
B) -18
C) -90
D) 90

Question 77

Determine whether the equation is true or false.

Question 78

Write the series in summation notation. Use the index i and let i begin at 1 in each summation.

A)
B)
C)
D)

Question 79

Write the series in summation notation. Use the index i and let i begin at 1 in each summation.
-6 + 7 - 8 + 9 - 10 + 11

A)
B)
C)
D)

Question 80

Write out all the terms of the series.

A)
B)
C)
D)