Deck 10: Sequences, Series and Probability

Question 1

Find the sum of the arithmetic sequence that satisfies the stated conditions.

A)
B)
C)
D)
E)

Answer 1

Question 2

Use the binomial theorem to expand and simplify.

A)
B)
C)
D)
E)

Answer 2

Question 3

Evaluate the expression. 6!0!

A)0
B)5,040
C)40,320
D)1
E)720

Answer 3

720

Question 4

Bode's sequence, defined by can be used to approximate distances of planets from the sun. These distances are measured in astronomical units, with 1 AU = 93,000,000 mi. For example, the third term corresponds to earth and the fifth term to the minor planet Ceres. Find the 4th term of the sequence.

A)
B)
C)
D)
E)

Question 5

A rubber ball is dropped from a height of 50 feet. If it rebounds approximately two-thirds the distance after each fall, use an infinite geometric series to approximate the total distance the ball travels.

A)200 ft
B)50 ft
C)250 ft
D)150 ft
E)400 ft

Question 6

Find the third term of the geometric sequence whose first two terms are 4 and 16.

A)28
B)40
C)1,024
D)64
E)256

Question 7

Use the binomial theorem to expand and simplify.

A)
B)
C)
D)
E)

Question 8

Use the binomial theorem to expand and simplify.

A)
B)
C)
D)
E)

Question 9

Find the number.

A)32
B)30
C)28
D)720
E)34

Question 10

Without expanding completely, find the term in the expansion of the expression that contains .

A)
B)
C)
D)
E)

Question 11

Use the principle of mathematical induction to find the equivalent expression for every positive integer n.

A)
B)
C)
D)
E)

Question 12

Find the third term of the sequence: is the number of decimal places in .

A)
B)
C)
D)
E)

Question 13

Evaluate the expression.

A)1
B)20
C)6
D)120
E)5

Question 14

Find the sum.

A)
B)
C)
D)
E)

Question 15

Find the third term of the recursively defined infinite sequence.

A)
B)
C)
D)
E)

Question 16

Use the principle of mathematical induction to find the factor of the expression. Hint:

A)
B)
C)
D)n
E)

Question 17

If seven basketball teams are in a tournament, find the number of different ways that first, second, and third place can be decided, assuming ties are not allowed.

A)42
B)210
C)6
D)1,680
E)840

Question 18

Find the fourth partial sum for the given sequence.

A)
B)
C)
D)
E)

Question 19

A company is to distribute $29,000 in bonuses to its top five salespeople. The fifth salesperson on the list will receive $4,600, and the difference in bonus money between successively ranked salespeople is to be constant. Find the bonus for each salesperson.

A)$6,400, $5,800, $5,200, $4,600, $4,000
B)$6,800, $6,700, $6,300, $5,900, $4,600
C)$7,000, $6,500, $6,100, $5,700, $4,600
D)$7,000, $6,400, $5,800, $5,200, $4,600
E)$6,800, $6,600, $6,200, $5,800, $4,600

Question 20

Express the sum in terms of n. (Hint: Use the theorem on sums to write the sum as . Next, use the following formulas and the theorem on the sum of a constant.)

A)
B)
C)
D)
E)

Question 21

A company is to distribute $34,000 in bonuses to its top five salespeople. The fifth salesperson on the list will receive $5,600, and the difference in bonus money between successively ranked salespeople is to be constant. Find the bonus for each salesperson.

A)$8,000, $7,600, $7,200, $6,800, $5,600
B)$8,000, $7,700, $7,300, $6,900, $5,600
C)$8,000, $7,500, $7,100, $6,700, $5,600
D)$7,400, $6,800, $6,200, $5,600, $5,000
E)$8,000, $7,400, $6,800, $6,200, $5,600

Question 22

Find the fourth partial sum for the given sequence.

A)
B)
C)
D)
E)

Question 23

Find the third term of the recursively defined infinite sequence.

A)
B)
C)
D)
E)

Question 24

Find the sum of the arithmetic sequence that satisfies the stated conditions.

A)
B)
C)
D)
E)

Question 25

In a round-robin tennis tournament, every player meets every other player exactly once. How many players can participate in a tournament of 55 matches?

A)22
B)11
C)10
D)14
E)55

Question 26

Find the third term of the geometric sequence whose first two terms are 3 and 9.

A)15
B)21
C)243
D)27
E)81

Question 27

Find the third term of the sequence: is the number of decimal places in .

A)
B)
C)
D)
E)

Question 28

Consider any four points such that no three are collinear. How many lines are determined?

A)24
B)2
C)12
D)6
E)4

Question 29

Express the sum in terms of n. (Hint: Use the theorem on sums to write the sum as . Next, use the following formulas and the theorem on the sum of a constant.)

A)
B)
C)
D)
E)

Question 30

Bode's sequence, defined by can be used to approximate distances of planets from the sun. These distances are measured in astronomical units, with 1 AU = 93,000,000 mi. For example, the third term corresponds to earth and the fifth term to the minor planet Ceres. Find the 5th term of the sequence.

A)
B)
C)
D)
E)

Question 31

Find the sum.

A)
B)
C)
D)
E)

Question 32

Evaluate the expression. 6!0!

A)24
B)5,040
C)720
D)0
E)1

Question 33

Use the principle of mathematical induction to find the factor of the expression. Hint:

A)
B)
C)
D)
E)n

Question 34

To win a state lottery game, a player must correctly select six numbers from the numbers 1 through 45. Find the total number of selections possible.

A)720
B)8,145,060
C)45
D)977,407,200
E)6

Question 35

A rubber ball is dropped from a height of 60 feet. If it rebounds approximately two-thirds the distance after each fall, use an infinite geometric series to approximate the total distance the ball travels.

A)300 ft
B)480 ft
C)240 ft
D)60 ft
E)180 ft

Question 36

Use the principle of mathematical induction to find the equivalent expression for every positive integer n.

A)
B)
C)
D)
E)

Question 37

A girl has four skirts, nine blouses and two sweaters. How many different skirt-blouse-sweater combinations can she wear?

A)72
B)15
C)82
D)36
E)68

Question 38

A single card is drawn from a deck. Find the probability that the card is either black or a face card.

A)
B)
C)
D)
E)

Question 39

Use the binomial theorem to expand and simplify.

A)
B)
C)
D)
E)

Question 40

Evaluate the expression.

A)1
B)5
C)12
D)4
E)24

Question 41

To win a state lottery game, a player must correctly select six numbers from the numbers 1 through 45. Find the total number of selections possible.

A)45
B)977,407,200
C)6
D)720
E)8,145,060

Question 42

Use the binomial theorem to expand and simplify.

A)
B)
C)
D)
E)

Question 43

Find the sum.

A)
B)
C)
D)
E)

Question 44

Consider any six points such that no three are collinear. How many lines are determined?

A)3
B)15
C)720
D)360
E)6

Question 45

A company is to distribute $28,000 in bonuses to its top five salespeople. The fifth salesperson on the list will receive $4,400, and the difference in bonus money between successively ranked salespeople is to be constant. Find the bonus for each salesperson.

A)$7,000, $6,400, $6,000, $5,600, $4,400
B)$6,200, $5,600, $5,000, $4,400, $3,800
C)$6,800, $6,300, $5,900, $5,500, $4,400
D)$7,000, $6,500, $6,100, $5,700, $4,400
E)$6,800, $6,200, $5,600, $5,000, $4,400

Question 46

Bode's sequence, defined by can be used to approximate distances of planets from the sun. These distances are measured in astronomical units, with 1 AU = 93,000,000 mi. For example, the third term corresponds to earth and the fifth term to the minor planet Ceres. Find the 5th term of the sequence.

A)
B)
C)
D)
E)

Question 47

Use the binomial theorem to expand and simplify.

A)
B)
C)
D)
E)

Question 48

Find the fourth partial sum for the given sequence.

A)
B)
C)
D)
E)

Question 49

A rubber ball is dropped from a height of 45 feet. If it rebounds approximately two-thirds the distance after each fall, use an infinite geometric series to approximate the total distance the ball travels.

A)45 ft
B)315 ft
C)225 ft
D)270 ft
E)180 ft

Question 50

A single card is drawn from a deck. Find the probability that the card is either red or a two.

A)
B)
C)
D)
E)

Question 51

Find the third term of the sequence: is the number of decimal places in .

A)
B)
C)
D)
E)

Question 52

A girl has three skirts, six blouses and two sweaters. How many different skirt-blouse-sweater combinations can she wear?

A)11
B)18
C)36
D)46
E)32

Question 53

Find the fifth term of the geometric sequence whose first two terms are 3 and 6.

A)18
B)32
C)96
D)9
E)48

Question 54

Find the third term of the recursively defined infinite sequence.

A)
B)
C)
D)
E)

Question 55

Find the sum of the arithmetic sequence that satisfies the stated conditions.

A)
B)
C)
D)
E)

Question 56

Use the principle of mathematical induction to find the equivalent expression for every positive integer n.

A)
B)
C)
D)
E)

Question 57

Find the number.

A)9
B)5
C)3
D)7
E)5,040

Question 58

If eleven basketball teams are in a tournament, find the number of different ways that first, second, and third place can be decided, assuming ties are not allowed.

A)110
B)6
C)7,920
D)990
E)11,880

Question 59

In a round-robin tennis tournament, every player meets every other player exactly once. How many players can participate in a tournament of 66 matches?

A)24
B)66
C)10
D)12
E)11

Question 60

Without expanding completely, find the term in the expansion of the expression that contains .

A)
B)
C)
D)
E)

Question 61

Use the binomial theorem to expand and simplify.

A)
B)
C)
D)
E)

Question 62

Evaluate the expression. 6!0!

A)120
B)720
C)40,320
D)0
E)1

Question 63

If ten basketball teams are in a tournament, find the number of different ways that first, second, and third place can be decided, assuming ties are not allowed.

A)720
B)90
C)6
D)7,920
E)5,040

Question 64

Consider any nine points such that no three are collinear. How many lines are determined?

A)36
B)362,880
C)4
D)181,440
E)9

Question 65

Express the sum in terms of n. (Hint: Use the theorem on sums to write the sum as . Next, use the following formulas and the theorem on the sum of a constant.)

A)
B)
C)
D)
E)

Question 66

In a round-robin tennis tournament, every player meets every other player exactly once. How many players can participate in a tournament of 78 matches?

A)26
B)14
C)13
D)78
E)12

Question 67

Use the principle of mathematical induction to find the factor of the expression. Hint:

A)
B)n
C)
D)
E)

Question 68

Use the binomial theorem to expand and simplify.

A)
B)
C)
D)
E)

Question 69

To win a state lottery game, a player must correctly select six numbers from the numbers 1 through 45. Find the total number of selections possible.

A)977,407,200
B)8,145,060
C)720
D)45
E)6

Question 70

Bode's sequence, defined by can be used to approximate distances of planets from the sun. These distances are measured in astronomical units, with 1 AU = 93,000,000 mi. For example, the third term corresponds to earth and the fifth term to the minor planet Ceres. Find the 6th term of the sequence.

A)
B)
C)
D)
E)

Question 71

Find the number of terms in the arithmetic sequence with the given conditions. ,

A)
B)
C)
D)
E)

Question 72

A girl has three skirts, ten blouses and five sweaters. How many different skirt-blouse-sweater combinations can she wear?

A)160
B)18
C)120
D)146
E)150

Question 73

Without expanding completely, find the term in the expansion of the expression that contains .

A)
B)
C)
D)
E)

Question 74

Find the specified term of the arithmetic sequence that has the two given terms.

A)
B)
C)
D)
E)

Question 75

A single card is drawn from a deck. Find the probability that the card is either red or a two.

A)
B)
C)
D)
E)

Question 76

Use the binomial theorem to expand and simplify.

A)
B)
C)
D)
E)

Question 77

Evaluate the expression.

A)120
B)1
C)5
D)20
E)6

Question 78

Find the number.

A)10
B)6
C)8
D)40,320
E)12

Question 79

Find the sum.

A)
B)
C)
D)
E)

Question 80

Find the fourth term of the recursively defined infinite sequence.

A)
B)
C)
D)
E)