Deck 7: Sequences, Series, and Probability

Question 1

Write an expression for the apparent nth term of the sequence.(Assume that n begins with 1.)

A)
B)
C)
D)
E)

Answer 1

D

Question 2

Determine whether the sequence is arithmetic.If so, find the common difference.(Assume that n begins with 1.)

A) -1
B) -8
C) 8
D) 1
E) not arithmetic

Answer 2

D

Question 3

Find the indicated term of the sequence.

A) 106
B) -110
C) -122
D) 18
E) -112

Answer 3

B

Question 4

Find a formula for a_n for the arithmetic sequence.

A)
B)
C)
D)
E)

Question 5

Find the sum.

A) 16
B) 32
C) 27
D) 11
E) 12

Question 6

Write the given series in summation notation.

A)
B)
C)
D)
E)

Question 7

Suppose that the annual payroll (in billions of dollars) of new car dealerships in the United States from 2000 to 2005 can be approximated by the model where represents the year, with corresponding to 2000.Find the total payroll from 2000 to 2005 by evaluating the sum Round your answer to the nearest ten million dollars.

A) $343.70 billion
B) $292.10 billion
C) $246.50 billion
D) $298.10 billion
E) $387.60 billion

Question 8

Simplify the factorial expression.

A) 11,880
B) 1320
C)
D) 132
E) 17,160

Question 9

A deposit of $1000 is made in an account that earns 4% interest compounded monthly.The balance in the account after n months is given by Find the balance in the account after 12 years by finding the 144th term of the sequence.Round to the nearest penny.

A) $283,661.80
B) $1614.78
C) $1609.42
D) $144,480.00
E) $1620.17

Question 10

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

A) 13, 18, 23, 28, 33
B) -8, -3, 2, 7, 12
C) -3, 10, 15, 20, 25
D) -3, 2, 7, 12, 17
E) -3, -11, -19, -27, -35

Question 11

Determine whether the sequence is arithmetic.If so, find the common difference. -2, -1, 0, 1, 2

A) -3
B) 1
C) -2
D) -1
E) not arithmetic

Question 12

Determine whether the sequence is arithmetic.If so, find the common difference.(Assume that n begins with 1.)

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

Question 13

Find the fifth term of the sequence that has the given nth term.

A)
B)
C)
D)
E)

Question 14

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

A) 4
B) 4ⁿ
C) 4ⁿ - 4^n-1
D) -4
E) not arithmetic

Question 15

Write the given series in summation notation.

A)
B)
C)
D)
E)

Question 16

Match the sequence with the graph of its first 10 terms.

A)
B)
C)
D)
E)

Question 17

Evaluate the series.

A)
B)
C)
D)
E)

Question 18

Write an expression for the most apparent nth term of the sequence.(Assume that begins with 1.)

A)
B)
C)
D)
E)

Question 19

Write an expression for the apparent nth term of the sequence.(Assume that n begins with 1.) -3, 2, 7, 12, 17

A)
B)
C)
D)
E)

Question 20

Suppose the ratio of alligators to pythons in a marshland from 2001 to 2008 can be approximated by the model where is the year, with corresponding to In 2006, the total number of alligators and pythons in the marsh was about 700.In that year, how many were alligators?

A) 62
B) 639
C) 57
D) 61
E) 638

Question 21

The seating section in a theater has 24 seats in the first row, 27 seats in the second row, and so on, increasing by 3 seats each row for a total of 19 rows.How many seats are in the tenth row?

A)
B)
C)
D)
E)

Question 22

Logs are stacked so that there are 21 logs in the bottom row, 20 logs in the second row from the bottom, and so on, decreasing by 1 log each row.How many logs are there in the first four rows from the bottom?

A) 140 logs
B) 60 logs
C) 78 logs
D) 153 logs
E) 165 logs

Question 23

Consider a job offer with a starting salary of $37,700 and a given annual raise of $2325.Determine the total compensation from the company through three full years of employment.

A) $366,700
B) $312,725
C) $77,725
D) $423,000
E) $120,075

Question 24

Use summation notation to write the sum below.

A)
B)
C)
D)
E)

Question 25

Find the nth term of the geometric sequence.

A)
B)
C)
D)
E)

Question 26

Find a formula for for the arithmetic sequence below.

A)
B)
C)
D)
E)

Question 27

Write the first five terms of the geometric sequence.

A) -5, -2, 1, 4, 7
B) -5, -15, -45, -135, -405
C)
D)
E)

Question 28

Find the nth term of the geometric sequence.

A)
B)
C)
D)
E)

Question 29

Match the geometric sequence with its graph from the choices below.

A)
B)
C)
D)
E)

Question 30

Determine whether the sequence is geometric.If so, find the common ratio. -5, -15, -45, -135, ...

A) 3
B) -5
C)
D) -3
E) not geometric

Question 31

Find the sum of the integers from 31 to 61.

A) 1891
B) 30
C) 2852
D) 1426
E) 3782

Question 32

Match the arithmetic sequence with its graph from the choices below.

A)
B)
C)
D)
E)

Question 33

Write the first five terms of the arithmetic sequence.

A) 3, 10, 17, 24, 31
B) -4, -11, -18, -25, -32
C) 3, -4, -11, -18, -25
D) 3, -21, 147, -1029, 7203
E) 3, -4, -1, 2, 5

Question 34

Find the partial sum.

A) -100,098
B) -99,102
C) -100,900
D) -101,103
E) -100,100

Question 35

A heavy object (with negligible air resistance) is dropped from a plane.During the first second of fall, the object falls 16.6 meters; during the second second, it falls 49.8 meters; during the third second, it falls 83.0 meters; and during the fourth second, it falls 116.2 meters.If this pattern continues, how many meters will the object fall in 10 seconds?

A) 813.4 meters
B) 597.6 meters
C) 1062.4 meters
D) 1660.0 meters
E) 1344.6 meters

Question 36

Find the indicated nth partial sum of the arithmetic sequence. 2.5, 3.8, 5.1, 6.4, ..., n = 100

A) 12,505
B) 6815
C) 6685
D) 6683.8
E) 6686.2

Question 37

Determine whether the sequence is geometric.If so, find the common ratio. -5, -2, 1, 4, ...

A) 3
B) -5
C)
D) -3
E) not geometric

Question 38

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

A)
B)
C)
D)
E)

Question 39

The annual sales (in millions of dollars) for a certain company from 2001 to 2006 can be approximated by the model where represents the year, with corresponding to 2001.Find the total sales from 2001 to 2005.Round to the nearest million.

A) $4119 million
B) $5427 million
C) $2972 million
D) $3295 million
E) $2003 million

Question 40

Use a graphing utility to graph the first 10 terms of the sequence.

A)
B)
C)
D)
E)

Question 41

Find the sum of the infinite geometric series below.

A)
B)
C)
D)
E)

Question 42

Find the sum of the finite geometric sequence.

A)
B)
C)
D)
E)

Question 43

Use the Binomial Theorem to expand the expression.Simplify your answer.

A)
B)
C)
D)
E)

Question 44

Evaluate using Pascal's triangle.Show your work.

Question 45

Use the Binomial Theorem to expand the complex number.Simplify your result.

A) -112 - 384i
B) -112 + 384i
C) 112 - 384i
D) 112 + 384i
E) 256

Question 46

Find the sum of the finite geometric series.Round to the nearest hundredth.

A)
B)
C)
D)
E)

Question 47

Write the rational number as the quotient of two integers in simplest form.

A)
B)
C)
D)
E)

Question 48

Use the Binomial Theorem to simplify the power of the complex number.

A)
B)
C)
D)
E)

Question 49

Find the sum of the infinite geometric series.

A)
B)
C)
D)
E) undefined

Question 50

Evaluate the binomial coefficient.

A)
B)
C)
D)
E)

Question 51

The annual profit (in millions of dollars) for a certain company from 2000 to 2005 can be approximated by the model where represents the year, with corresponding to 2000.Use the formula for the sum of a finite geometric sequence to approximate the total profit earned during this six-year period.Round to the nearest ten-thousand dollars.

A) $4466.74 million
B) $4805.90 million
C) $3631.55 million
D) $3292.39 million
E) $2676.77 million

Question 52

Use the Binomial Theorem to expand and simplify the expression.

A)
B)
C)
D)
E)

Question 53

Use the Binomial Theorem to expand and simplify the expression.

A)
B)
C)
D)
E)

Question 54

Evaluate using Pascal's triangle.Show your work.

Question 55

Expand the binomial by using Pascal's triangle to determine the coefficients.Show your work.

Question 56

Use summation notation to write the sum.

A)
B)
C)
D)
E)

Question 57

Find the rational number representation of the repeating decimal.

A)
B)
C)
D)
E)

Question 58

Calculate the binomial coefficient:

A) 60
B) 15
C) 10
D) 1
E) 0

Question 59

Find the sum of the finite geometric series.

A)
B)
C)
D)
E)

Question 60

Find the sum of the infinite geometric series.

A)
B)
C)
D)
E)

Question 61

Find the coefficient a of the term in the expansion of the binomial. Binomial Term

A) a = 12
B)
C) a = 32
D)
E)

Question 62

Find the number of distinguishable permutations of the group of letters.

A)
B)
C)
D)
E)

Question 63

Decide which of the scenarios below should be counted using permutations or combinations. Scenario I:
Number of ways 7 people can line up in a row for concert tickets.
Scenario II:
Number of ways a team of 8 students can be selected from a group of 50 people.
Scenario III:
Number of ways a jury of 11 people can be selected from a group of 40 people.

A) Scenarios II and III are combinations and scenario I is a permutation.
B) All scenarios are permutations.
C) All scenarios are combinations.
D) Scenario III is a combination and scenarios I and II are permutations.
E) Scenarios I and II are combinations and scenario III is a permutation.

Question 64

At a high school cafeteria, diners can choose one vegetable from a choice of 4 vegetables, one meat from a choice of 3 meats, one serving of bread from among 4 breads, and a dessert from among 3 desserts.How many meal configurations are possible?

A) 14
B) 144
C) 4
D) 48
E) 36

Question 65

Find the specified nth term in the expansion of the binomial.

A)
B)
C)
D)
E)

Question 66

Twenty-four students, of whom four are seniors, are selected as semifinalists for a literary award.Of the twenty-four students, twelve finalists will be selected.In how many ways can the twelve finalists contain two seniors?

A)
B)
C)
D)
E)

Question 67

In how many ways can a 12-question true-false exam be answered? (Assume that no questions are omitted.)

A) 4096
B) 65,536
C) 524,288
D) 1024
E) 1,048,576

Question 68

A combination lock will open when the right choice of three numbers (from 1 to 36) is selected.How many different lock combinations are possible?

A) 139,968
B) 1296
C) 36
D) 108
E) 46,656

Question 69

Two six-sided dice are tossed.Find the probability that the sum is prime or even.

A)
B)
C)
D)
E)

Question 70

In a certain state, each automobile license plate number consists of two letters followed by a five-digit number.To avoid confusion between "O" and "zero" and "I" and "one", the letters "O" and "I" are not used.How many distinct license plate numbers can be formed?

A) 13,824,000
B) 57,600,000
C) 331,776,000
D) 5,760,000
E) 138,240,000

Question 71

Evaluate the expression.

A) 3
B) 9
C) 6
D) 5
E) 8

Question 72

There are 13 patients in Dr.Ziglar's waiting room.Dr.Ziglar can see 6 patients before lunch.In how many different orders can Dr.Ziglar see 6 of the patients before lunch?

A) 1716
B) 8,648,640
C) 78
D) 6
E) 1,235,520

Question 73

Twenty-four students are selected as semifinalists for a literary award.Of the twenty-four students, fourteen finalists will be selected.In how many ways can fourteen finalists be selected from the twenty-four students?

A) 38,760
B) 319,770
C) 4,457,400
D) 1,961,256
E) 116,280

Question 74

Evaluate: ₉P₆

A) 84
B) 504
C) 60,480
D) 54
E) undefined

Question 75

A coin is tossed three times.Find the probability of getting two heads.

A)
B)
C)
D)
E)

Question 76

A computer randomly generates an integer from 1 through 50.Find the probability of the event that a multiple of 8 is generated.

A)
B)
C)
D)
E)

Question 77

A computer manufacturer offers a computer system with five different disk drives, two different monitors, and three different keyboards.How many different computer systems could a consumer purchase from this manufacturer?

A) 24
B) 40
C) 30
D) 18
E) 75

Question 78

Determine the number of ways a computer can randomly generate an integer divisible by 4 from 1 through 15.

A) 7
B) 3
C) 11
D) 5
E) 9

Question 79

Eight cards are chosen at random from a standard deck of playing cards.In how many ways can the cards be chosen if all eight cards are diamonds.

A)
B)
C)
D)
E)

Question 80

A state lottery game requires a person to select nine different numbers from thirty-six numbers.The order of the selection is not important.In how many ways can this be done?

A)
B)
C)
D)
E)