9.1 Sequences
534
9.1 Sequences
Multiple Choice
Identify the choice that best completes the statement or answers the question.
____ 1. Write the first five terms of the sequence.
a.
b.
c.
d.
e.
____ 2. Write the first five terms of the sequence.
a.
b.
c.
d.
e.
535 Chapter 9: Infinite Series
____ 3. Write the first three terms of the sequence.
a.
b.
c.
d.
e.
____ 4. Match the sequence with its graph.
a. d.
b. e.
9.1 Sequences
536
c.
____ 5.
Graph the sequence
.
a.
d.
b. e.
537 Chapter 9: Infinite Series c.
____ 6. Match the sequence with its graph.
a. d.
b. e.
9.1 Sequences
538
c.
____ 7. Match the sequence with its graph.
a. d.
b. e.
539 Chapter 9: Infinite Series
c.
____ 8. Write the next two apparent terms of the sequence .
a.
b.
c.
d.
e.
____ 9. Determine the convergence or divergence of the sequence with the given nth term. If the
sequence converges, find its limit.
The sequence converges to –1.
The sequence converges to 0.
The sequence diverges.
The sequence converges to 1.
The sequence diverges to 1.
9.1 Sequences
540
____ 10.
Determine the convergence or divergence of the sequence with the given nth term. If
the sequence converges, find its limit.
The sequence diverges.
The sequence converges to 2.
The sequence converges to –1.
The sequence converges to 1.
The sequence converges to 0.
11.
Write an expression for the nth term of the sequence
.
12.
Write an expression for the nth term of the sequence
.
____ 13.
Consider the sequence
whose nth term is given by
where
P is the principal,
is the account balance in dollars after n months, and r is the interest rate
compounded annually. Find the fourth term of the sequence if
and
. Round your
answer to two decimal places.
$9,296.08
$9,599.41
$9,396.38
$9,196.59
$9,236.29
541
Chapter 9: Infinite Series
____
14.
A deposit of $225 is made at the beginning of each month into an account at an
annual interest rate of 3% compounded monthly. The balance in the account after n months is
. Find the balance in the account after 4 years by computing the 48th
term of the sequence. Round your answer to two decimal places.
$11,488.17
$905.64
$9,172.05
$24,404.88
$1,818.08
____ 15. A government program that currently costs taxpayers $2.5 billion per year is cut back by 30
percent per year. Write an expression for the amount budgeted for this program after n years.
a.
b.
c.
d.
e.
____ 16. A government program that currently costs taxpayers $3.5 billion per year is cut back by 30
percent per year. Compute the budget after the fifth year. Round your answer to the nearest integer.
$1,552,968,594
$272,160,000
$8,505,000
$1,146,880,000
$588,245,000
____ 17.
If the rate of inflation is
% per year and the average price of a car is currently
$40,000, the average price after n years is
. Compute the average price after 6
years. Round your answer to two decimal places.
$32,301.59
$49,170.21
$248,400.00
$45,937.01
$231,600.00
9.1 Sequences
542
9.1
Sequences
1.
10.
12.
13.
16.
17.
543 Chapter 9: Infinite Series
9.2 Series and Convergence
Multiple Choice
Identify the choice that best completes the statement or answers the question.
____ 1. Write the first five terms of the sequence of partial sums.
a.
b.
c.
d.
e.
____ 2. Write the first five terms of the sequence of partial sums.
a.
b.
c.
d.
e.
9.2 Series and Convergence
544
____ 3.
Write the first five terms of the sequence of partial sums.
a.
b.
c.
d.
e.
____ 4. True or false. The infinite series .
false
true
____ 5. Find the sum of the convergent series.
4
36
9
27
45
____ 6. Find the sum of the convergent series.
a.
545 Chapter 9: Infinite Series
b.
c.
d.
e.
____ 7. Find the sum of the convergent series.
a.
b.
c.
d.
e.
____ 8. Find the sum of the convergent series
a.
b.
c.
d.
e.
9.2 Series and Convergence
546
____ 9. Find the sum of the convergent series .
a.
b.
c.
d.
e.
____ 10. Write the repeating decimal as a geometric series.
a.
b.
c.
d.
e.
547 Chapter 9: Infinite Series
____ 11. True or false. The series is convergent.
false
true
____ 12. True or false. The series is divergent.
false
true
____ 13. Determine the convergence or divergence of the series.
cannot be determined from the methods in the chapter
Diverges
Converges
____ 14. Find all values of x for which the series converges.
a.
b.
c.
d.
e.
____ 15. Find all values of x for which the series converges. For these values of x, write the sum
of the series as a function of x.
a.
b.
c.
9.2 Series and Convergence
548
The series diverges for all x.
16.
Suppose an electronic games manufacturer producing a new product estimates the
annual sales to be 4,000 units. Each year 20% of the units that have been sold will become
inoperative. So, 4,000 units will be in use after 1 year,
units will be in use
after 2 years, and so on. How many units will be in use after n years?
units
units
units
units
units
17.
Suppose the annual spending by tourists in a resort city is $100 million.
Approximately 90% of that revenue is again spent in the resort city, and of that amount approximately
90% is again spent in the same city, and so on. Write the expression that gives the total amount of
spending generated by the $100 million after n years.
a.
million dollars
b.
million dollars
c.
million dollars
d.
million dollars
e.
million dollars
____ 18.
Suppose the annual spending by tourists in a resort city is $100 million.
Approximately 75% of that revenue is again spent in the resort city, and of that amount approximately
75% is again spent in the same city, and so on. Summing all of this spending indefinitely, leads to the
geometric series
$800 million
$401 million
$200 million
$801 million
$400 million
. Find the sum of this series.
549
Chapter 9: Infinite Series
____
19.
Suppose a ball is dropped from a height of 16 feet. Each time it drops h feet, it
rebounds 0.85h feet. Find the total distance traveled by the ball. Round your answer to two
decimal places.
229.33 feet
410.67 feet
181.33 feet
197.33 feet
213.33 feet
____ 20. Suppose the winner of a $4,000,000 sweepstakes will be paid $100,000 per year for 40
years, starting a year from now. The money earns 5% interest per year. The present value of the
winnings is Compute the present value using the formula for the nth partial
sum of a geometric series. Round your answer to two decimal places.
$6,852,274.09
$1,959,646.05
$4,568,182.73
$1,246,221.03
$1,715,908.64
____ 21. Suppose you go to work at a company that pays $0.08 for the first day, $0.16 for the
second day, $0.32 for the third day, and so on. If the daily wage keeps doubling, what would your
total income be for working 29 days? Round your answer to two decimal places.
$21,474,836.48
$10,737,418.24
$42,949,672.88
$171,798,691.52
$85,899,345.76
9.2 Series and Convergence
550
9.2 Series and Convergence
Answer Section
2.
5.
9.
11.
14.
15.
17.
20.
551 Chapter 9: Infinite Series
9.3 The Integral Test and p-Series
Multiple Choice
Identify the choice that best completes the statement or answers the question.
____ 1. Use the Integral Test to determine the convergence or divergence of the series.
diverges
Integral Test inconclusive
converges
____ 2. Use the Integral Test to determine the convergence or divergence of the series.
converges
diverges
Integral Test inconclusive
____ 3. True or false: The series converges.
false
true
____ 4. True or false: The series converges.
true
false
____ 5. True or false: The series converges.
false
true
9.3 The Integral Test and p-Series
552
____ 6.
Use the Integral Test to determine the convergence or divergence of the series.
diverges
Integral Test inconclusive
converges
____ 7. Use the Integral Test to determine the convergence or divergence of the series.
diverges
converges
Integral Test inconclusive
____ 8. True or false: The series converges.
true
false
____ 9. True or false: The series diverges.
false
true
____ 10. Use Theorem 9.11 to determine the convergence or divergence of the series.
converges
diverges
Theorem 9.11 inconclusive
553 Chapter 9: Infinite Series
____ 11. Use Theorem 9.11 to determine the convergence or divergence of the series.
diverges
converges
Theorem 9.11 inconclusive
____ 12. Use Theorem 9.11 to determine the convergence or divergence of the series.
converges
diverges
Theorem 9.11 inconclusive
____ 13. Sketch the graph of the sequence of partial sum of the series .
a. d.