Deck 13: Sequences and Series

Question 1

What is the present value of a lottery prize of 2 million dollars, paid out at a rate of $40,000 per year for 50 years? Assume an annual interest rate of 3%. Round to the nearest dollar.

Answer 1

$1,060,066

Question 2

A patient takes 400 mg of a pain-killing drug twice a day. Every 12 hours, the patient's body metabolizes 20% of the drug present. If the patient continues to take the drug indefinitely, how many mg of the drug will remain in the patient's body in the long run? Round to 2 decimal places.

Answer 2

2000.00

Question 3

Find the sum of the series , for
.

A)
B)
C)
D)

Answer 3

Question 4

What is ? Round to 2 decimal places.

Question 5

Subtract the following two equations and solve for S: Assume x is not equal to 1.

A)
B)
C)
D)

Question 6

Let , with . As , what happens to S?

A)
B)
C)
D)

Question 7

An athlete is offered a signing bonus of $2 million per year for 7 years. If the interest rate is 4% per year, compounded annually, what is the present value of this bonus? Round to the nearest dollar.

Question 8

A plaintiff is awarded a settlement of $15,000 per year (paid at the beginning of the year) for the rest of his life. Assuming 3.7% annual interest, how much money would the defendant have to put aside now in order to ensure that the settlement would be paid (no matter how many years the plaintiff lived)? In other words, what is the present value of the settlement if the plaintiff may live indefinitely? Round to the nearest dollar.

Question 9

Does the infinite geometric series
converge or diverge?

Question 10

Write as a fraction.

Question 11

An employee is offered a salary of $100,000 per year for 6 years. What is the present value of the contract on the date of the first payment if the interest rate is 2.3% per year, compounded continuously. Round your answer to two decimal places.

Question 12

Write as a fraction.

Question 13

What is the present value of a $1000 bond which pays $40 each year for 15 years, with the first payment one year from now? Assume the interest rate is 5.1% per year compounded annually.

Question 14

What is the present value of a $1000 bond which pays $45 each year for 15 years, with the first payment one year from now? Assume the interest rate is 5.5% per year compounded annually.

A) $899.62
B) $451.69
C) $904.10
D) $895.38

Question 15

Find the sum . Round your answer to 3 decimal places.

Question 16

Your doctor tells you to take 37 mg of a certain drug every 12 hours. It is known that only 6% of the drug is still in the body at the end of 12 hours. What quantity of the drug is in the body right after taking the 11th dose? Give your answer correct to 3 decimal places.

Question 17

Your doctor tells you to take 38 mg of a certain drug every 12 hours. It is known that only 6% of the drug is still in the body at the end of 12 hours. Assuming you continue to take the drug, what happens to the drug level in the long run? Give your answer correct to 3 decimal places.

Question 18

For what values of x does the sum converge?

Question 19

For what values of x does the sum converge?

Question 20

Find the sum of the series:

Question 21

If you were to fill out a pedigree chart, the first column would have one name (yours), the second column would have two names (your parents), the third column would have 4 names (your grandparents), etc. How many names would be on the chart if there were 13 columns total?

Question 22

The repeating decimal 0.848484. . . can be written as an infinite geometric series 0.84 + 0.0084 + 0.000084 + . . . . Use this fact to find a fraction that is equivalent to 0.848484. . . . Your answer should be of the form "A/B".

Question 23

If is a geometric series, give its ratio. If not, enter "not geometric"

Question 24

Find to 3 decimal places.

Question 25

If , then a = _____, b = _____, and c = ______.

Question 26

Is the series arithmetic, geometric, or neither?

Question 27

Is the series arithmetic, geometric, or neither?

Question 28

Is a geometric series?

Question 29

Find the sum of the series
.

Question 30

A new employee is offered two salary packages. Both start with an initial salary of $44,000. Package A offers a $2500 increase each year. Package B offers a 4.5% increase each year. After 7 years, the annual salary with package A would be $_______ and the annual salary with package B would be $_______. Round both answers to the nearest dollar.

Question 31

Find the sum of the series
. Round to 2 decimal places.

Question 32

Does ?

Question 33

Evaluate to 3 decimal places.

Question 34

To save for their child's college education, parents put $250 at the beginning of each month into an account that pays 6.5% annual interest, compounded monthly. How much will they have saved if they do this for 18 years? Round to the nearest cent.

Question 35

To save for their child's college education, parents put $100 at the beginning of each month into an account that pays 5.5% annual interest, compounded monthly. They do this for 18 years. How much money per month would they have had to save if they needed the same total amount in 18 years, but their account only paid 2.5% annual interest, compunded monthly? Round to the nearest cent.

Question 36

A patient takes 400 mg of a pain-killing drug twice a day. Every 12 hours, the patient's body metabolizes 30% of the drug present. How many mg of the drug remain in the patient's body after 6 days (right after the 12^th dose)? Round to 2 decimal places.

Question 37

A patient takes 600 mg of a pain-killing drug twice a day. Every 12 hours, the patient's body metabolizes 25% of the drug present. If the patient stops taking the drug after 1 week, how many mg of the drug remain in the patient's body 3 days after that? Round to 2 decimal places.

Question 38

The population of Arizona rose from 5,130,635 in 2000 to 5,939,292 in 2005. Assuming a constant percent annual growth rate, what is the population expected to be in 2015? Round to the nearest whole number.

Question 39

The population of Arizona rose from 5,130,635 in 2000 to 5,939,292 in 2005. Assuming a constant percent growth rate, in what year is the population first expected to exceed 11 million?

Question 40

Does ?

Question 41

Does ?

Question 42

What is the sum of the first 18 positive even integers?

Question 43

The following table shows the enrollment in a private college for the years 1996 to 2005. Interpret these figures as partial sums, , of terms of a sequence,
, where n is the number of years since 1995 (so
, etc.).
Which of the following gives the change in enrollment between 1997 and 1998?

A)
B)
C)
D)

Question 44

The following table shows the enrollment in a private college for the years 1996 to 2005. Interpret these figures as partial sums, , of terms of a sequence, , where n is the number of years since 1995 (so , etc.).
Which of the following gives the total enrollment in 2004?

A)
B)
C)
D)

Question 45

The following table shows the enrollment in a private college for the years 1996 to 2005. Interpret these figures as partial sums, , of terms of a sequence, , where n is the number of years since 1995 (so , etc.). Which of the following gives the average enrollment between 2000 and 2003?

A)
B)
C)
D)

Question 46

The following table shows the enrollment in a private college for the years 1996 to 2005. Interpret these figures as partial sums, , of terms of a sequence,
, where n is the number of years since 1995 (so, etc.). Which of the following gives the average change in enrollment between 1998 and 2002?

A)
B)
C)
D)

Question 47

A person decides to walk for 15 minutes one day, and then increases his walks by 1.5 minutes each day for a month. Let be the sequence showing the length of time he walks each day, where is the length of time he walks on day n, and let be the sequence of partial sums. What is ?

Question 48

Does ?

Question 49

If , then a = _____, b = _____, and c = _____.

Question 50

What is ?

Question 51

Does ?

Question 52

A child building a tower with blocks places 17 blocks in the first row, 16 blocks in the second row, 15 blocks in the third row, and so forth. How many blocks are in the tower if it has 12 rows total?

Question 53

How many terms are there in the series ?

Question 54

If denotes your total earnings after n weeks of work, what is the average amount of money you earned each week for the first 8 weeks?

A)
B)
C)
D)

Question 55

The time it takes an employee to assemble a bicycle is 56 minutes the first time he does it. The second time, it take him 55 minutes; the third time it takes 54 minutes, and so on. If this trend continues, how many minutes will it take him to assemble the 15^th bicycle?

Question 56

The time it takes an employee to assemble a bicycle is 55 minutes the first time he does it. The second time, it take him 52 minutes; the third time it takes 49 minutes, and so on. If this trend continues and there are 15 bicycles to assemble, it should take him a total of _____ hours and _____ minutes.

Question 57

Which of the following is the correct expansion of
?

A)
B)
C)
D)

Question 58

Evaluate the following sum :

Question 59

Find the sum of the first 200 odd integers.

Question 60

Write using sigma notation.

Question 61

Write using sigma notation.

Question 62

Is the following sequence arithmetic, geometric, or neither?1, 2, 4, 8, . . .

Question 63

Is the following sequence arithmetic, geometric, or neither?

Question 64

Is the following sequence arithmetic, geometric, or neither?

Question 65

For the arithmetic sequence , suppose . If , what is d?

Question 66

For the arithmetic sequence , suppose . What is ?

Question 67

For the arithmetic sequence , suppose and the partial sum . What is ?

Question 68

A sequence can be defined by a recurrence relation, which gives the first term, , and a formula for finding in terms of the previous term, . For the recurrence relation below, what is ?

Question 69

A sequence Can be defined by a recurrence relation, which gives the first term, , and a formula for finding In terms of the previous term, For the recurrence relation below, what is the formula for the general term?

A)
B)
C)
D)

Question 70

Is an arithmetic sequence?

Question 71

Consider the sequence involving sums of odd integers. What is the 40^th term of this sequence (i.e. the sum of the first 40 odd numbers)?

Question 72

A person decides to walk for 16 minutes one day, and then increases his walks by 1.5 minutes each day for a month. Let be the sequence showing the length of time he walks each day, where is the length of time he walks on day n. What is ?

Question 73

Let be an arithmetic sequence with and . What is ?

Question 74

Let be an arithmetic sequence with and . What is ?

Question 75

Let be a geometric sequence with and . What is ?

Question 76

If denotes your total earnings after n weeks of work, is the amount you earned during the 10^th week given by ?

Question 77

Is the sequence arithmetic, geometric, neither, or both?

Question 78

Is the sequence arithmetic, geometric, neither, or both?

Question 79

What is the 13^th term of the sequence 1, 6, 11, 16, . . .? The sequence is either arithmetic or geometric.

Question 80

What is the 9^th term of the sequence 1, 3, 9, 27, 81, . . .? The sequence is either arithmetic or geometric.