Deck 15: Sequences, Series, and the Binomial Theorem

Question 1

Write the next three terms of the sequence.
-6, -9, -12, -15, ...

A) -18, -21, -24
B) 18, 21, 24
C) -21, -24, -27
D) -12, -9, -6

Answer 1

-18, -21, -24

Question 2

Write the first five terms of the sequence whose nth term is shown.
an = n - 5

A) -20, -15, -10, -5, 0
B)
C) -4, -3, -2, -1, 0
D) -5, -4, -3, -2, -1

Answer 2

-4, -3, -2, -1, 0

Question 3

Write the first five terms of the sequence whose nth term is shown.
an = 4n - 1

A) -3, -7, -11, -15, -19
B) 5, 9, 13, 17, 21
C) 3, 7, 11, 15, 19
D) 3, 4, 5, 6, 7

Answer 3

3, 7, 11, 15, 19

Question 4

Write the first five terms of the sequence whose nth term is shown.

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

Question 5

Write the first five terms of the sequence whose nth term is shown.

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

Question 6

Evaluate the series.

A) 60
B) 45
C) 30
D) 90

Question 7

Write out the series.

A) 4 + 5 + 6 + 7 + ...
B) 3 + 4 + 5 + 6
C) 7 + 8 + 9 + 10
D) 4 + 5 + 6 + 7

Question 8

Write the first five terms of the sequence whose nth term is shown.
an = 2n

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

Question 9

Find the indicated term of the sequence whose nth term is shown.

A) 1
B) 15
C) 39
D) 23

Question 10

Evaluate the series.

A) 24
B) 30
C) 16
D) 28

Question 11

Write the first five terms of the sequence whose nth term is shown.
an = n2n+ 2

A)
B)
C)
D)

Question 12

Write out the series.

A) 75
B) 1 + 3 + 9 + 15 + 21 + 27
C) 3 + 9 + 15 + 21 + 27 + 33
D) 3 + 9 + 15 + 21 + 27 + 33 + ...

Question 13

Write the next three terms of the sequence.

A) 10, 7, 4
B) 16, 19, 25
C) 16, 19, 22
D) 19, 22, 25

Question 14

Write the first five terms of the sequence whose nth term is shown.

A) 1, 12 , 13 , 14 , 15
B)
C) 4, 1, 49 , 14 , 254
D)

Question 15

Consider the following squares. For the nth square, the length of each side is n.
i) Find the perimeters of the first 4 squares, then list the perimeters in a sequence.
ii) Find the general term for the perimeter of the nth square in the sequence. Use pn for the perimeter.

Question 16

Write the next three terms of the sequence.
4, 16, 64, 256, . . .

A) 1024, 4096, 16,384
B) 1280, 1536, 1792
C) 1025, 4097, 16,385
D) 4096, 16,384, 65,536

Question 17

Find the indicated term of the sequence whose nth term is shown.

A) 15
B) 210
C) 225
D) 195

Question 18

Write the next three terms of the sequence.

A)
B)
C)
D)

Question 19

Write out the series.

A)
B)
C)
D)

Question 20

Find the indicated term of the sequence whose nth term is shown.

A) 26
B) 25
C) 23
D) 29

Question 21

For the given general term an, write an expression using ∑ to represent the indicated partial sum.
third partial sum

A)
B)
C)
D) i

Question 22

Find the common difference of the sequence.

A) 6
B) -2
C) -6
D) 2

Question 23

Find the arithmetic mean of the following set of data.
4, 16, 64, 256, 1024

A) 1364
B) 272.8
C) 341
D) 227.33

Question 24

Evaluate the series.

A)
B)
C)
D)

Question 25

For the given general term an, write an expression using ∑ to represent the indicated partial sum.
third partial sum

A)
B)
C)
D)

Question 26

Find the first and third partial sums, s1 and s3, for the sequence

A)
B)
C)
D)

Question 27

Find the first and third partial sums, s1 and s3, for the sequence

A) -3, 9
B) -3, -1
C) -3, -7
D) -3, -3

Question 28

For the given general term an, write an expression using ∑ to represent the indicated partial sum.

A)
B)
C)
D)

Question 29

Find the common difference of the sequence.

A) 635
B) -6
C) 6
D) -635

Question 30

Find the common difference of the sequence.

A) -4
B) -12
C) 12
D) -8

Question 31

Find the common difference of the sequence.

A) 4
B) 3
C) 1
D) 0.75

Question 32

Evaluate the series.

A) 30
B) 18
C) 20
D) 14

Question 33

Find the arithmetic mean of the following set of data.
80, 90, 100, 110, 120

A) 500
B) 100
C) 110
D) 90

Question 34

For the set of values x find the following.

A) 35
B) 40
C) 8
D) 41

Question 35

Find the first and third partial sums, s1 and s3, for the sequence

A)
B)
C)
D)

Question 36

Find the arithmetic mean of the following set of data.
1, 5, 9, 13, 17

A) 7.5
B) 11.25
C) 45
D) 9

Question 37

Evaluate the series.

A) 75
B) 24
C) 36
D) 62

Question 38

Evaluate the series.

A) -52
B) -9
C) -34
D) -60

Question 39

For the given general term an, write an expression using ∑ to represent the indicated partial sum.

A)
B)
C)
D)

Question 40

For the set of values x find the following.

A) 32
B) 6
C) -10
D) 42

Question 41

Find the indicated quantity of the arithmetic sequence.

A) 52
B) 35
C) 34
D) 1

Question 42

Write the expression for the general (or nth) term, an, of the arithmetic sequence. Then, find the indicated term of the
arithmetic sequence.

A)
B)
C)
D)

Question 43

Find the common difference of the sequence.

A)
B) -3
C)
D)

Question 44

Write the expression for the general (or nth) term, an, of the arithmetic sequence. Then, find the indicated term of the
arithmetic sequence.

A)
B)
C)
D)

Question 45

Find the indicated quantity of the arithmetic sequence.

A) 779
B) -775
C) 773
D) -781

Question 46

Write the first five terms of the arithmetic sequence with the given term and common difference.

A) 6, 10, 14, 18, 22
B) 10, 14, 18, 22, 26
C) 6, 9, 12, 15, 18
D) 0, 6, 10, 14, 18

Question 47

Find the indicated quantity of the arithmetic sequence.
a

A) 24
B) 23
C) 17
D) 22

Question 48

Write the expression for the general (or nth) term, an, of the arithmetic sequence.

A)
B)
C)
D)

Question 49

Write the expression for the general (or nth) term, an, of the arithmetic sequence.

A)
B)
C)
D)

Question 50

Write the expression for the general (or nth) term, an, of the arithmetic sequence. Then, find the indicated term of the
arithmetic sequence.

A)
B)
C)
D)

Question 51

Find the sum, of the sequence.

A) 27
B) 63
C) 238
D) 119

Question 52

Find the common difference of the sequence.

A) 4.35
B) 5.63
C) 13.05
D) 3.2625

Question 53

Write the first five terms of the arithmetic sequence with the given term and common difference.

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

Question 54

Find the sum, of the sequence.

A) 135
B) -51
C) - 135
D) -85

Question 55

Write the expression for the general (or nth) term, an, of the arithmetic sequence.

A)
B)
C)
D)

Question 56

Write the first five terms of the arithmetic sequence with the given term and common difference.

A)
B)
C)
D)

Question 57

Find the indicated quantity of the arithmetic sequence.

A) 59
B) -59
C) 51
D) -64

Question 58

Write the expression for the general (or nth) term, an, of the arithmetic sequence.

A)
B)
C)
D)

Question 59

Write the expression for the general (or nth) term, an, of the arithmetic sequence. Then, find the indicated term of the
arithmetic sequence.

A)
B)
C)
D)

Question 60

Write the expression for the general (or nth) term, an, of the arithmetic sequence.

A)
B)
C)
D)

Question 61

Solve the problem.
Deborah is considering a job that offers a monthly starting salary of $3000 and guarantees her a monthly raise of $170 during her first year on the job. Find her monthly salary at the end of her first year.

A) $4870
B) $4700
C) $3170
D) $5040

Question 62

For the geometric sequence, find the common ratio, r.

A)
B) 3
C) 2
D)

Question 63

Find the sum, of the sequence.
-1, -5, -9, -13, . . ., -77

A) -770
B) -820
C) -780
D) -81

Question 64

Determine the first five terms of the geometric sequence.

A) 6, 30, 150, -750, 3750
B) -5, -30, 150, -750, 3750
C) 6, 1, -4, -9, -14
D) 6, -30, 150, -750, 3750

Question 65

For the geometric sequence, find the common ratio, r.

A) 4
B)
C) 2
D) 6

Question 66

For the geometric sequence, find the common ratio, r.

A)
B)
C) 53
D)

Question 67

Find the sum, of the sequence.
5, 1, -3, -7, . . ., -231

A) -6900
B) -6780
C) -6772
D) -235

Question 68

Solve the problem.
A school auditorium has 40 rows with 27 seats in the first row, 31 in the second row, 35 in the third row, and so forth. How many seats are in the auditorium?

A) 8560 seats
B) 8400 seats
C) 4200 seats
D) 4280 seats

Question 69

For the geometric sequence, find the common ratio, r.
6, -1.8, 0.54, -0.162, . . .

A) -1.8
B) -0.3
C) -0.03
D) -3

Question 70

Find the sum, of the sequence.
2, 4, 6, 8, . . ., 110

A) 3135
B) 3080
C) 3087
D) 112

Question 71

Determine the first five terms of the geometric sequence.

A) -7, -10, -13, -16, -19
B) -3, 21, -63, 189, -567
C) -7, 21, -63, 189, -567
D) -7, -21, -63, 189, -567

Question 72

For the geometric sequence, find the common ratio, r.
3, 9, 27, 81, 243, . . .

A) 9
B)
C) 27
D) 3

Question 73

Find the sum, of the sequence.
Find the sum of the first 70 positive odd integers.

A) 4904
B) 4830
C) 4900
D) 4826

Question 74

Solve the problem.
A grocery store display of apples has a total of 16 rows. The bottom row requires 104 apples. Each successive row requires 5 less apples than the prior one. How many apples are required to build the display?

A) 2264 apples
B) 2128 apples
C) 1064 apples
D) 1024 apples

Question 75

Find the sum, of the sequence.

A) 660
B) 616
C) 720
D) 480

Question 76

Determine the first five terms of the geometric sequence.

A)
B)
C) 9, 27, 81, 243, 729
D)

Question 77

Find the sum, of the sequence.
12, 21, 30, 39, . . ., 633

A) 22,584
B) 22,890
C) 642
D) 22,575

Question 78

Find the sum, of the sequence.
Find the sum of the odd integers between 36 and 78.

A) 1311
B) 1197
C) 1254
D) 1140

Question 79

Determine the first five terms of the geometric sequence.

A) 3, 7, 11, 15, 19
B) 3, 12, 48, 192, 768
C) 4, 12, 36, 108, 324
D) 12, 48, 192, 768, 3072

Question 80

For the geometric sequence, find the common ratio, r.
1, -3, 9, -27, 81, . . .

A) 9
B) -3
C) 3
D) -4