Deck 11: Sequences, Series, and Probability

Question 1

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

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

Answer 1

1, -6, -13, -20, -27

Question 2

Find the twentieth term of the arithmetic sequence. 8, 0, -8

A)-24
B)-144
C)-120
D)-80
E)-112

Answer 2

-144

Question 3

Write the given series in summation notation.

A)
B)
C)
D)
E)

Answer 3

Question 4

Find the seventh term of the sequence that has the given nth term below. is the digit in the nth place in the decimal expansion of .

A)1
B)0
C)8
D)7
E)6

Question 5

Evaluate the series.

A)128
B)8
C)32
D)2
E)64

Question 6

Find the n th partial sum of the arithmetic sequence. ;

A)12
B)-273
C)-468
D)0
E)-560

Question 7

Simplify the factorial expression.

A)
B)11,880
C)110
D)990
E)7920

Question 8

Find the sum.

A)30
B)8
C)18
D)20
E)12

Question 9

Find the n th term of the geometric sequence. 5, -10, 20,...

A)
B)
C)
D)
E)

Question 10

Find the third term of the sequence that has the given n th term.

A)7
B)3
C)8
D)4
E)5

Question 11

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

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

Question 12

Joey bought a new tractor for use in his landscaping business. He expects that the use of the tractor will generate $ 3500 of revenue in the first year with an increase in revenue of $ 500 per year for subsequent years. If the tractor's useful lifetime is 8 years, how much revenue will Joey receive from the use of the tractor?

A)$ 7500
B)$ 46,000
C)$ 171,000
D)$ 35,000
E)$ 42,000

Question 13

Evaluate the factorial expression.

A)3432
B)1
C)2002
D)14
E)1001

Question 14

Evaluate the series.

A)25
B)95
C)0
D)1225
E)775

Question 15

Find the n th partial sum of the arithmetic sequence.

A)
B)
C)
D)
E)

Question 16

Write the given series in summation notation.

A)
B)
C)
D)
E)

Question 17

The seating section in a theater has 29 seats in the first row, 34 seats in the second row, and so on, increasing by 5 seats each row for a total of 13 rows. How many seats are in the tenth row?

A)84
B)74
C)44
D)49
E)64

Question 18

Write the given series in summation notation.

A)
B)
C)
D)
E)

Question 19

Find the n th term of the arithmetic sequence. -1, 7, 15

A)
B)
C)
D)
E)

Question 20

Logs are stacked so that there are 24 logs in the bottom row, 23 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 five rows from the bottom?

A)110 logs
B)147 logs
C)180 logs
D)129 logs
E)69 logs

Question 21

If , use mathematical induction to show that for all positive integers n .

Question 22

Use the Binomial Theorem to expand and simplify the expression.

A)
B)
C)
D)
E)

Question 23

Find the sixth term without expanding.

A)
B)
C)
D)
E)252

Question 24

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

A)52+ 47i
B)351+ 272i
C)15+ 8i
D)17- 8i
E)161+ 240i

Question 25

Use the Binomial Theorem to expand and simplify the expression.

A)
B)
C)
D)
E)

Question 26

Use mathematical induction to prove the formula for every positive integer n . Show all your work.

Question 27

Find the sum of the infinite geometric series.

A)
B)
C)
D)
E)

Question 28

To save for the replacement of a computer, a business deposits $300 at the end of each month into an account that earns 5% annual interest compounded monthly. Find the future value of the ordinary annuity in 4 years.

A)$15922.70
B)$15936.42
C)$15832.05
D)$15904.47
E)$15931.84

Question 29

Find the sum of the infinite geometric series.

A)
B)
C)
D)
E)

Question 30

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

A)-98.80
B)13223.94
C)1858.99
D)36.05
E)260.80

Question 31

Suppose that $500,000 of counterfeit money is currently in circulation and that each time the counterfeit money is used, 35% of it is detected and removed from circulation. How much counterfeit money, to the nearest thousand dollars, is used in transactions before all of it is removed from circulation?

A)$769,000
B)$1,346,000
C)$1,154,000
D)$705,000
E)$1,410,000

Question 32

Find the sum of the finite geometric series.

A)-600
B)-5460
C)-195
D)-147615
E)-15

Question 33

Find the fifth term without expanding.

A)
B)
C)
D)
E)

Question 34

Prove the inequality for the indicated integer values of n .

Question 35

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

A)
B)
C)
D)
E)

Question 36

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

A)
B)
C)
D)
E)

Question 37

A letter listing the names and addresses of 8 people was sent to 3 other people, who were asked to send $5 to the name at the top of the list and then remove that person's name. Each recipient then added his or her name to the bottom of the list and sent the letter to five friends. Assuming no one broke the chain, how much money would each recipient of the letter receive?

A)$1,171,875
B)$98,304
C)$32,805
D)$1,944
E)$2,560

Question 38

Find the sum of the infinite geometric series below.

A)
B)
C)
D)
E)

Question 39

Sometimes a city will argue that having a professional sports franchise in the city will contribute to economic growth. The rationale for this statement is based on the multiplier effect. Suppose a city estimates that a professional sports franchise will create $45 million of additional income and that a person receiving a portion of this money will spend 80% and save 20%. Assuming the multiplier effect model is accurate, what is the net effect of the $45 million? Round to the nearest hundred thousand.

A)$450.0 million
B)$225.0 million
C)$281.3 million
D)$262.5 million
E)$356.3 million

Question 40

Find the n th term of the geometric sequence.

A)
B)
C)
D)
E)

Question 41

Eight cards are chosen at random from a standard deck of playing cards. In how many ways can the cards be chosen if three or more cards are kings.

A)6,849,216
B)7,043,796
C)73,629,072
D)194,580
E)294,516,288

Question 42

Determine the sample space for the experiment. Three prize winners are selected from six people: A, B, C, D, E, and F.

Question 43

A car holds seven passengers, four in the front seat and three in the back seat. How many different seating arrangements of seven people are possible if two people refuses to sit in front and one person refuses to sit in back?

A)24
B)2,520
C)864
D)6
E)1,260

Question 44

A six-digit binary number is a sequence of six digits, each consisting of 0 or 1. For instance, 101010 and 011011 are six-digit binary numbers. How many six-digit binary numbers are possible?

A)32
B)256
C)128
D)16
E)64

Question 45

The numbers 1, 2, 3, 4, 5, 6, 7, 8, 9 are to be arranged. How many different arrangements are possible under the condition that all odd numbers come first?

A)144
B)36
C)4
D)2880
E)576

Question 46

Six cards are chosen at random from a standard deck of playing cards. In how many ways can the cards be chosen if all six cards are clubs.

A)1,716
B)5,089,630
C)24
D)28,276
E)720

Question 47

Nineteen students are selected as semifinalists for a literary award. Of the nineteen students, ten finalists will be selected. In how many ways can ten finalists be selected from the nineteen students?

A)3,003
B)19,448
C)43,758
D)92,378
E)8,008

Question 48

Seven cards are chosen at random from a standard deck of playing cards. In how many ways can the cards be chosen if all seven cards are the same suit.

A)6,864
B)1,716
C)112
D)16
E)133,784,560

Question 49

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

A)1,040,754
B)474,474
C)1,106,105
D)1,098,669
E)834,834

Question 50

Thirty people enter a tennis tournament. How many different first-round matches are possible if each player can be matched with any other player?

A)105
B)435
C)155,117,520
D)32,768
E)870

Question 51

An ice cream store offers 33 flavors of ice cream. How many different triple-decker cones are possible? Note: Assume that different orders of the same flavors are not different cones. Thus a scoop of rocky road followed by two scoops of mint chocolate is the same as one scoop of mint chocolate followed by one scoop of rocky road followed by a second scoop of mint chocolate.

A)32,736
B)6,545
C)33
D)16,368
E)6,017

Question 52

A shipment of eleven calculators contains seven defective calculators. Four calculators are chosen from the shipment. Find the probability that exactly four are defective.

A)
B)
C)
D)
E)

Question 53

In how many ways can a student answer a 32-question true-false test if the student randomly marks 6 of the questions true and 26 of the questions false?

A)347,373,600
B)28,048,800
C)201,376
D)906,192
E)225,792,840

Question 54

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

A)6,172,530
B)817,190
C)40,116,600
D)21
E)293,930

Question 55

Use the sample space defined by the experiment of tossing a fair coin four times. Express the event that there are exactly two tails as a subset of the sample space.

A){HHHH}
B){TTTT, TTTH, TTHT, THTT, HTTT}
C){HHTT, HTHT, THHT, HTTH, THTH, TTHH}
D){TTTT}
E){HHHH, HHHT, HHTH, HTHH, THHH}

Question 56

A single number is chosen from the digits 1, 2, 3, 4, 5, and 6. Find the probability that the number is an odd number or a number divisible by 3.

A)
B)
C)
D)
E)

Question 57

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

A)222
B)736,281
C)177,100
D)13,983,816
E)2,324,784

Question 58

Six cards are chosen at random from a standard deck of playing cards. In how many ways can the cards be chosen if exactly four cards are aces.

A)1,128
B)1,035
C)1,275
D)1,326
E)1,225

Question 59

Nine weightlifters are competing in the dead-lift competition. In how many ways can the weightlifters finish first, second, and third (no ties)?

A)729
B)3
C)504
D)27
E)6

Question 60

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

A)12
B)45
C)18
D)30
E)27

Question 61

As a test for extrasensory perception (ESP), eight cards, four black and four white, are shuffled, and then a person looks at each card. In another room, the ESP subject attempts to guess whether the card is black or white. The ESP subject must guess black four times and white four times. If the ESP subject has no extrasensory perception, what is the probability that the subject will correctly name six of the eight cards? Round to the nearest thousandth.

A)0.014
B)0.229
C)0.450
D)0.667
E)0.039

Question 62

A quality control inspector receives a shipment of 20 computer monitors. From the 20 monitors, the inspector randomly chooses 6 for inspection. If the probability of a monitor being defective is 0.12, what is the probability that at least one of the monitors chosen by the inspector is defective? Round to the nearest hundredth.

A)0.54
B)0.39
C)0.69
D)0.41
E)0.44

Question 63

Twelve persons are arranged in a line. What is the probability that three specific people are standing next to each other?

A)
B)
C)
D)
E)

Question 64

A club has nine members. One member starts a rumor by telling it to a second club member, who repeats the rumor to a third member, and so on. At each stage, the recipient of the rumor is chosen at random from the nine club members. What is the probability that the rumor will be told eight times without returning to the originator? Round to the nearest hundredth.

A)0.49
B)0.44
C)0.55
D)0.70
E)0.79

Question 65

One card is randomly drawn from a standard deck of playing cards where aces are not considered numbered cards and are the highest card in the suit. The card is replaced and another card is drawn. What is the probability that both cards drawn are even numbered cards?

A)
B)
C)
D)
E)

Question 66

An airline estimates that 80% of the people who make a reservation for a certain flight will actually show up for the flight. Suppose the airline sells 22 tickets on this flight and the plane has room for 18 passengers. What is the probability that 19 or more people with tickets will show up for the flight? Round to the nearest hundredth.

A)0.13
B)0.40
C)0.33
D)0.27
E)0.07