Deck 9: Sequences, Series, and Probability

Question 1

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

Answer 1

not arithmetic

Question 2

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

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

Answer 2

-1562

Question 3

Find the sum of the finite geometric sequence.

A)5824
B)
C)
D)
E)

Answer 3

Question 4

Find the indicated nth term of the geometric sequence.

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

Question 5

Find the sum of the infinite series.

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

Question 6

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 7

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 8

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 9

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 10

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

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

Question 11

Use summation notation to write the sum.

A)
B)
C)
D)
E)

Question 12

Calculate the binomial coefficient:

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

Question 13

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

A)
B)
C)
D)
E)

Question 14

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

A)
B)
C)
D)
E)

Question 15

Calculate the binomial coefficient:

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

Question 16

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

A)
B)
C)
D)
E)

Question 17

Find P_k+1 for the given P_k.

A)
B)
C)
D)
E)

Question 18

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

Question 19

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 20

Find the sum.

A)
B)1
C)
D)
E)

Question 21

Use summation notation to write the sum.

A)
B)
C)
D)
E)

Question 22

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 23

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 24

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

A)
B)
C)
D)
E)

Question 25

Find the sum of the infinite series.

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

Question 26

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 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

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 29

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 30

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 31

Find the sum of the finite geometric sequence.

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

Question 32

Find the sum.

A)1
B)
C)
D)
E)

Question 33

A)
B)
C)
D)
E)

Question 34

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 35

Use the Binomial Theorem to expand and simplify the expression.

A)
B)
C)
D)
E)

Question 36

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

A)
B)
C)
D)
E)

Question 37

Evaluate using a graphing utility:

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

Question 38

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 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

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 41

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

A)
B)
C)
D)
E)

Question 42

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 43

A)
B)
C)
D)
E)

Question 44

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 45

Use the Binomial Theorem to expand and simplify the expression.

A)
B)
C)
D)
E)

Question 46

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 47

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

A)
B)
C)
D)
E)

Question 48

Calculate the binomial coefficient:

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

Question 49

Find the sum of the infinite series.

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

Question 50

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 51

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 52

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

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

Question 53

Calculate the binomial coefficient:

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

Question 54

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 55

Evaluate using a graphing utility:

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

Question 56

Find P_k+1 for the given P_k.

A)
B)
C)
D)
E)

Question 57

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 58

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 59

Find the sum.

A)
B)
C)1
D)
E)

Question 60

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 61

Use summation notation to write the sum.

A)
B)
C)
D)
E)

Question 62

Evaluate using a graphing utility:

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

Question 63

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 64

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 65

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 66

Evaluate the sum.

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

Question 67

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 68

Find the indicated nth term of the geometric sequence.

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

Question 69

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

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

Question 70

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

A)
B)
C)
D)
E)

Question 71

Calculate the binomial coefficient:

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

Question 72

Calculate the binomial coefficient:

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

Question 73

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

A)
B)
C)
D)
E)

Question 74

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

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

Question 75

Use the Binomial Theorem to expand and simplify the expression.

A)
B)
C)
D)
E)

Question 76

Find the sum of the finite geometric sequence.

A)
B)
C)1936
D)
E)

Question 77

A)
B)
C)
D)
E)

Question 78

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 79

Evaluate the sum.

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

Question 80

Find P_k+1 for the given P_k.

A)
B)
C)
D)
E)