Deck 9: Sequences, Series, and Probability

Question 1

Find a quadratic model for the sequence with the indicated terms.

A)
B)
C)
D)
E)

Answer 1

Question 2

The first two terms of the arithmetic sequence are given. Find the indicated term.

A) -37
B) -31
C) -25
D) 19
E) 24

Answer 2

-25

Question 3

Determine whether the sequence is geometric. If so, find the common ratio. 3, -1, -5, -9,...

A) not geometric
B) 3
C)
D) -4
E) 4

Answer 3

not geometric

Question 4

Find P_k+1 for the given P_k.

A)
B)
C)
D)
E)

Question 5

Find the sum of the infinite series.

A) undefined
B)
C) 3
D)
E)

Question 6

Determine whether the sequence is arithmetic. If so, find the common difference. 5, 25, 125, 625, 3125

A) not arithmetic
B) (
)
C) 5
D)
E) -5

Question 7

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)
B)
C)
D)
E)

Question 8

Find the indicated nth term of the geometric sequence. 5th term:

A)
B)
C)
D)
E)

Question 9

Find the sum using the formulas for the sums of powers of integers.

A) -4686
B) -1155
C) -1562
D) 198
E) -407

Question 10

Calculate the binomial coefficient:

A) 20
B) 18
C) 120
D) 0
E) 1

Question 11

Use summation notation to write the sum.

A)
B)
C)
D)
E)

Question 12

Determine whether the sequence is arithmetic. If so, find the common difference. 3, 1, -1, -3, -5

A) 5
B) -2
C) not arithmetic
D) 3
E) 2

Question 13

Calculate the binomial coefficient:

A) 1
B) 35
C) 0
D) 21
E) 210

Question 14

Write an expression for the apparent nth term of the sequence. (Assume that n begins with 1.) 1, 6, 11, 16, 21

A)
B)
C)
D)
E)

Question 15

Find the indicated nth term of the geometric sequence.

A) 972
B) 3072
C) 12,288
D) 2916
E) 23

Question 16

Find the indicated nth partial sum of the arithmetic sequence. -2.1, 2.5, 7.1, 11.7, ...., n=90

A) -7996.5
B) 18,241
C) 18,648
D) 18,227
E) 18,234

Question 17

Find the sum.

A)
B) 1
C)
D)
E)

Question 18

Find the indicated partial sum of the series. fourth partial sum

A)
B)
C)
D)
E)

Question 19

Find the sum of the finite geometric sequence.

A) 5824
B)
C)
D)
E)

Question 20

Write the first five terms of the sequence. (Assume that n begins with 1.)

A) 13, 18, 23, 28, 33
B) 13, 21, 29, 37, 45
C) -3, 2, 12, 12, 17
D) 13, 10, 15, 20, 25
E) 8, 13, 18, 23, 28

Question 21

Find the indicated partial sum of the series. fourth partial sum

A)
B)
C)
D)
E)

Question 22

The first two terms of the arithmetic sequence are given. Find the indicated term.

A) -50
B) -76
C) -46
D) -64
E) -70

Question 23

Determine whether the sequence is geometric. If so, find the common ratio. -2, -7, -12, -17,...

A) -2
B) not geometric
C)
D) 5
E) -5

Question 24

Write an expression for the apparent nth term of the sequence. (Assume that n begins with 1.) 9, 12, 15, 18, 21

A)
B)
C)
D)
E)

Question 25

Use the Binomial Theorem to expand and simplify the expression.

A)
B)
C)
D)
E)

Question 26

Evaluate using a graphing utility:

A) 116,280
B) 1,860,480
C) 100
D) 15,504
E) undefined

Question 27

Find the number of diagonals of a undecagon (11 sides). (A line segment connecting any two nonadjacent vertices is called a diagonal of the polygon.)

A) 110
B) 121
C) 44
D) 22
E) 11

Question 28

The probability that a basketball player will make a given free throw is . To find the probability that the player makes exactly 9 out of her next 10 free throws, evaluate the term in the expansion of . Round to four decimal places.

A) 0.0403
B) 0.0016
C) 0.0605
D) 0.0010
E) 0.1008

Question 29

Find the sum.

A) 1
B)
C)
D)
E)

Question 30

Find the sum of the finite geometric sequence.

A)
B)
C) 233,017
D)
E)

Question 31

Find the indicated nth partial sum of the arithmetic sequence. -1.5, 1.1, 3.7, 6.3, ...., n=70

A) 6178.1
B) -3440.5
C) 6169.9
D) 6356
E) 6174

Question 32

Use summation notation to write the sum.

A)
B)
C)
D)
E)

Question 33

Find the indicated nth term of the geometric sequence. 6th term:

A)
B)
C)
D)
E)

Question 34

Determine whether the sequence is arithmetic. If so, find the common difference. 4, 16, 64, 256, 1024

A) not arithmetic
B) ( )
C) 4
D) -4
E)

Question 35

Find the sum of the infinite series.

A)
B) 3
C) undefined
D)
E)

Question 36

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)
B)
C)
D)
E)

Question 37

Determine whether the sequence is arithmetic. If so, find the common difference. 8, 10, 12, 14, 16

A) 8
B) 6
C) -2
D) 2
E) not arithmetic

Question 38

A)
B)
C)
D)
E)

Question 39

Find the indicated nth term of the geometric sequence.

A) -327,680
B) -81,920
C) 1,562,500
D) 23
E) -312,500

Question 40

Write the first five terms of the sequence. (Assume that n begins with 1.)

A) 4, 9, 14, 19, 24
B) 1, 6, 16, 16, 21
C) 9, 13, 17, 21, 25
D) 9, 10, 15, 20, 25
E) 9, 14, 19, 24, 29

Question 41

Evaluate using a graphing utility:

A) 3003
B) 32,760
C) undefined
D) 75
E) 360,360

Question 42

Find the sum.

A)
B)
C) 1
D)
E)

Question 43

The first two terms of the arithmetic sequence are given. Find the indicated term.

A) 42
B) -36
C) -42
D) 48
E) 36

Question 44

Determine whether the sequence is arithmetic. If so, find the common difference. 8, 13, 18, 23, 28

A) 3
B) 5
C) 8
D) -5
E) not arithmetic

Question 45

Write an expression for the apparent nth term of the sequence. (Assume that n begins with 1.) 5, 8, 11, 14, 17

A)
B)
C)
D)
E)

Question 46

Find the sum using the formulas for the sums of powers of integers.

A) -110
B) -182
C) 390
D) -72
E) -546

Question 47

The probability that a basketball player will make a given free throw is . To find the probability that the player makes exactly 8 out of her next 10 free throws, evaluate the term in the expansion of . Round to four decimal places.

A) 7.5497
B) 0.0000
C) 0.0001
D) 0.3020
E) 4.8318

Question 48

Write the first five terms of the sequence. (Assume that n begins with 1.)

A) -15, -22, -36, -36, -43
B) 8, 1, -6, -13, -20
C) 1, -14, -21, -28, -35
D) 1, -6, -13, -20, -27
E) 1, 9, 17, 25, 33

Question 49

Determine whether the sequence is arithmetic. If so, find the common difference. 5, 25, 125, 625, 3125

A) 5
B) (
)
C)
D) -5
E) not arithmetic

Question 50

Use the Binomial Theorem to expand and simplify the expression.

A)
B)
C)
D)
E)

Question 51

Find the number of diagonals of a nonagon (9 sides). (A line segment connecting any two nonadjacent vertices is called a diagonal of the polygon.)

A) 27
B) 18
C) 81
D) 9
E) 72

Question 52

Calculate the binomial coefficient:

A) 342
B) 38
C) 1
D) 0
E) 171

Question 53

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)
B)
C)
D)
E)

Question 54

Calculate the binomial coefficient:

A) 1
B) 126
C) 45
D) 15,120
E) 0

Question 55

A)
B)
C)
D)
E)

Question 56

Find P_k+1 for the given P_k.

A)
B)
C)
D)
E)

Question 57

Find the indicated nth partial sum of the arithmetic sequence. 1.9, 4.8, 7.7, 10.6, ...., n=20

A) 419
B) 647
C) 589
D) 590
E) 588

Question 58

Find the indicated partial sum of the series. third partial sum

A)
B)
C)
D)
E)

Question 59

Find a quadratic model for the sequence with the indicated terms.

A)
B)
C)
D)
E)

Question 60

Find the sum of the infinite series.

A) undefined
B)
C) 4
D)
E)

Question 61

Determine whether the sequence is geometric. If so, find the common ratio. -1, -3, -5, -7,...

A) -2
B) -1
C)
D) 2
E) not geometric

Question 62

Find the number of diagonals of a nonagon (9 sides). (A line segment connecting any two nonadjacent vertices is called a diagonal of the polygon.)

A) 27
B) 72
C) 81
D) 9
E) 18

Question 63

Evaluate the sum.

A) 120
B) 20
C) 21
D) 60
E) 56

Question 64

Calculate the binomial coefficient:

A) 120
B) 20
C) 5
D) 1
E) 0

Question 65

Evaluate using a graphing utility:

A) 5005
B) 360,360
C) 3,603,600
D) 90
E) undefined

Question 66

Find the indicated nth term of the geometric sequence. 4th term:

A)
B)
C)
D)
E)

Question 67

The probability that a basketball player will make a given free throw is . To find the probability that the player makes exactly 9 out of her next 10 free throws, evaluate the term in the expansion of . Round to four decimal places.

A) 0.0016
B) 0.0605
C) 0.0010
D) 0.0403
E) 0.1008

Question 68

Calculate the binomial coefficient:

A) 15,120
B) 45
C) 126
D) 1
E) 0

Question 69

Find the sum of the finite geometric sequence.

A)
B)
C) 1936
D)
E)

Question 70

Write the first six terms of the sequence defined by the function. f(n) = 6n(n - 1)

A) -12, -36, 72, -120, -180, 0
B) 12, 36, 72, 120, 180, 252
C) 12, 36, 72, 120, 180, 504
D) -12, 0, 36, 72, 120, 180
E) 0, 12, 36, 72, 120, 180

Question 71

Find the next term of the sequence. 8, 27, 64, 125, ...

A) 216
B) 1,296
C) 224
D) 252
E) none of these

Question 72

Use the Binomial Theorem to expand and simplify the expression.

A)
B)
C)
D)
E)

Question 73

Find the indicated nth term of the geometric sequence.

A) 29
B) 20,480
C) 81,920
D) 62,500
E) 312,500

Question 74

Evaluate the sum.

A) 8
B) 300
C) 2,405
D) 3
E) 2,400

Question 75

Find the next term of the sequence. 5, 12, 19, 26, ...

A) 66
B) 33
C) 40
D) 29
E) 39

Question 76

Use summation notation to write the sum.

A)
B)
C)
D)
E)

Question 77

Find a quadratic model for the sequence with the indicated terms.

A)
B)
C)
D)
E)

Question 78

A)
B)
C)
D)
E)

Question 79

Find P_k+1 for the given P_k.

A)
B)
C)
D)
E)

Question 80

Find the sum using the formulas for the sums of powers of integers.

A) -374
B) -1482
C) -120
D) 78
E) -494