The common difference is
.
Therefore, the sequence is arithmetic.
10-1 Sequences as Functions
Determine whether each sequence is
arithmetic. Write yes or no.
Find the next four terms of each arithmetic
sequence. Then graph the sequence.
26. 10, 2, –6, –14, …
22. –9, –3, 0, 3, 9
SOLUTION: Subtract any term from the term directly after it.
SOLUTION: Subtract any term from the term directly after it.
There is no common difference.
Therefore, the sequence is not arithmetic.
The common difference is –8.
Therefore, this sequence is arithmetic.
To find the next term, add –8 to the last term.
24. SOLUTION: Subtract any term from the term directly after it.
–14 + (–8) = –22
–22 + (–8) = –30
–30 + (–8) = –38
–38 + (–8) = –46
Graph the sequence.
The common difference is
.
Therefore, the sequence is arithmetic.
Find the next four terms of each arithmetic
sequence. Then graph the sequence.
26. 10, 2, –6, –14, …
SOLUTION: Subtract any term from the term directly after it.
28. –19, –2, 15, …
SOLUTION: Subtract any term from the term directly after it.
The common difference is –8.
Therefore, this sequence is arithmetic.
To find the next term, add –8 to the last term.
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–14 + (–8) = –22
–22 + (–8) = –30
–30 + (–8) = –38
The common difference is 17.
Therefore, the sequence is arithmetic.
To find the next term, add 17 to the last term.
15 + 17 = 32
32 + 17 = 49
49 + 17 = 66
66 + 17 = 83
Page 1
10-1 Sequences as Functions
28. –19, –2, 15, …
SOLUTION: Subtract any term from the term directly after it.
30. SOLUTION: Subtract any term from the term directly after it.
The common difference is 17.
Therefore, the sequence is arithmetic.
To find the next term, add 17 to the last term.
15 + 17 = 32
32 + 17 = 49
49 + 17 = 66
66 + 17 = 83
The common difference is –1.
Therefore, the sequence is arithmetic.
To find the next term, add −1 to the last term.
Graph the sequence.
Graph the sequence.
30. SOLUTION: Subtract any term from the term directly after it.
The common difference is –1.
Therefore, the sequence is arithmetic.
32. CCSS SENSE-MAKING Mario began an exercise
program to get back in shape. He plans to row 5
minutes on his rowing machine the first day and
increase his rowing time by one minute and thirty
seconds each day.
a. How long will he row on the 18th day?
To find the next term, add −1 to the last term.
b. On what day will Mario first row an hour or
more?
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c. Is it reasonable for this pattern to continue
indefinitely? Explain.
Page 2
10-1 Sequences as Functions
32. CCSS SENSE-MAKING Mario began an exercise
program to get back in shape. He plans to row 5
minutes on his rowing machine the first day and
increase his rowing time by one minute and thirty
seconds each day.
a. How long will he row on the 18th day?
b. On what day will Mario first row an hour or
more?
c. Sample answer: It is unreasonable because there
are only so many hours in the day that can be
dedicated to rowing.
Determine whether each sequence is
geometric. Write yes or no.
34. 124, 186, 248, …
SOLUTION: Find the ratio of the consecutive terms.
c. Is it reasonable for this pattern to continue
indefinitely? Explain.
SOLUTION: a. Given a 1 = 5, d = 1.5 and n = 18.
Find a 18.
Since the ratios are not the same, the sequence is not
geometric.
36. 162, 108, 72, …
SOLUTION: Find the ratio of the consecutive terms.
Therefore he will row for 30 minutes and 30 seconds
on the 38th day.
b. Given a 1 = 5, d = 1.5 and a n = 60.
Find n.
Since the ratios are same, the sequence is geometric.
38. –4, –2, 0, 2, …
SOLUTION: Find the ratio of the consecutive terms.
Mario will first row an hour or more on the 38th day.
Since the ratios are not same, the sequence is not
geometric.
c. Sample answer: It is unreasonable because there
are only so many hours in the day that can be
dedicated to rowing.
Determine whether each sequence is
geometric. Write yes or no.
34. 124, 186, 248, …
SOLUTION: Find the ratio of the consecutive terms.
Find the next three terms of the sequence.
Then graph the sequence.
40. 18, 12, 8, …
SOLUTION: Find the ratio of the consecutive terms.
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Since the ratios are same, the sequence is geometric.
Since the ratios are not same, the sequence is not
10-1geometric.
Sequences as Functions
Find the next three terms of the sequence.
Then graph the sequence.
40. 18, 12, 8, …
42. 81, 108, 144, …
SOLUTION: Find the ratio of the consecutive terms.
SOLUTION: Find the ratio of the consecutive terms.
Since the ratios are same, the sequence is geometric
To find the next term, multiply the previous term by
Since the ratios are same, the sequence is geometric.
.
To find the next term, multiply the previous term by
.
Graph the sequence.
Graph the sequence.
44. 1, 0.1, 0.01, 0.001, …
42. 81, 108, 144, …
SOLUTION: Find the ratio of the consecutive terms.
SOLUTION: Find the ratio of the consecutive terms.
Since the ratios are same, the sequence is geometric.
To find the next term, multiply the previous term by
0.1.
Since the ratios are same, the sequence is geometric
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To find the next term, multiply the previous term by
.
10-1 Sequences as Functions
44. 1, 0.1, 0.01, 0.001, …
Determine whether each sequence is
arithmetic, geometric, or neither. Explain your
reasoning.
SOLUTION: Find the ratio of the consecutive terms.
46. 1, –2, –5, –8, …
SOLUTION: Subtract each term from the term directly after it.
Since the ratios are same, the sequence is geometric.
To find the next term, multiply the previous term by
0.1.
The common difference is –3.
Therefore, the sequence is arithmetic.
To find the common ratio, find the ratio of the
consecutive terms.
Graph the sequence.
Since the ratios are not same, the sequence is not
geometric.
48. Determine whether each sequence is
arithmetic, geometric, or neither. Explain your
reasoning.
SOLUTION: Subtract each term from the term directly after it.
46. 1, –2, –5, –8, …
SOLUTION: Subtract each term from the term directly after it.
There is no common difference.
Therefore, this sequence is not arithmetic.
To find the common ratio, find the ratio of the
consecutive terms.
The common difference is –3.
Therefore, the sequence is arithmetic.
To find the common ratio, find the ratio of the
consecutive terms.
The common ratio is
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.
Since the ratios are the same, the sequence is
geometric.
Page 5
Since the ratios are not same, the sequence is not
geometric.
10-1 Sequences as Functions
Since the ratios are not same, the sequence is not
geometric.
52. DEPRECIATION Tammy’s car is expected to
depreciate at a rate of 15% per year. If her car is
currently valued at $24,000, to the nearest dollar,
how much will it be worth in 6 years?
48. SOLUTION: Subtract each term from the term directly after it.
SOLUTION: Substitute 0.15, 6 and 24000 for r, t and P in
then evaluate.
There is no common difference.
Therefore, this sequence is not arithmetic.
To find the common ratio, find the ratio of the
consecutive terms.
The worth of the car will be about $9052 after 6
years.
53. CCSS REGULARITY When a piece of paper is
folded onto itself, it doubles in thickness. If a piece of
paper that is 0.1 mm thick could be folded 37 times,
how thick would it be?
The common ratio is
.
Since the ratios are the same, the sequence is
geometric.
50. 6, 9, 14, 21, …
SOLUTION: Given a 0 = 0.1, n = 37 and r = 2.
Find a 37.
SOLUTION: Subtract each term from the term directly after it.
The thickness would be about 13,744 km.
There is no common difference.
Therefore, the sequence is not arithmetic.
To find the common ratio, find the ratio of the
consecutive terms.
Since the ratios are not same, the sequence is not
geometric.
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Cognero
52. DEPRECIATION
car is expected to
depreciate at a rate of 15% per year. If her car is
currently valued at $24,000, to the nearest dollar,
54. REASONING Explain why the sequence 8, 10, 13,
17, 22 is not arithmetic.
SOLUTION: Sample answer: The consecutive terms do not share
a common difference. For instance, 22 – 17 = 5,
while 17 – 13 = 4.
55. OPEN ENDED Describe a real-life situation that
can be represented by an arithmetic sequence with a
common difference of 8.
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SOLUTION: Sample answer: A babysitter earns $20 for cleaning
SOLUTION: Sample answer: The consecutive terms do not share
a common difference. For instance, 22 – 17 = 5,
17 – 13as
= 4.
10-1while
Sequences
Functions
55. OPEN ENDED Describe a real-life situation that
can be represented by an arithmetic sequence with a
common difference of 8.
SOLUTION: Sample answer: A babysitter earns $20 for cleaning
the house and $8 extra for every hour she watches
the children.
Sample answer:
Let d = 5.
Therefore, the terms are –3, 2, 7.
57. ERROR ANALYSIS Brody and Gen are
determining whether the sequence 8, 8, 8,… is
arithmetic, geometric, neither, or both. Is either of
them correct? Explain your reasoning.
56. CHALLENGE The sum of three consecutive terms
of an arithmetic sequence is 6. The product of the
terms is –42. Find the terms.
SOLUTION: Let x be the first term in the arithmetic sequence.
Therefore, the next two terms should be x + d and x
+ 2d.
SOLUTION: Sample answer: Neither; the sequence is both
arithmetic and geometric.
58. OPEN ENDED Find a geometric sequence, an
arithmetic sequence, and a sequence that is neither
geometric nor arithmetic that begins 3, 9,… .
Sample answer:
Let d = 5.
Therefore, the terms are –3, 2, 7.
57. ERROR ANALYSIS Brody and Gen are
determining whether the sequence 8, 8, 8,… is
arithmetic, geometric, neither, or both. Is either of
them correct? Explain your reasoning.
SOLUTION: Sample answer: geometric: 3, 9, 27, 81, 243, … arithmetic: 3, 9, 15, 21, 27, … neither geometric nor
arithmetic: 3, 9, 21, 45, 93, ...
59. REASONING If a geometric sequence has a ratio r
such that
, what happens to the terms as n
increases? What would happen to the terms if
?
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SOLUTION: Sample answer: If a geometric sequence has a ratio
r such that
, as n increases, the absolute value
of the terms will decrease and approach zero
because they are continuously being multiplied by a
fraction. When
, the absolute value of the
terms will increase and approach infinity because
they are continuously being multiplied by a valuePage 7
greater than 1.
SOLUTION: Sample answer: geometric: 3, 9, 27, 81, 243, … arithmetic: 3, 9, 15, 21, 27, … neither geometric nor
3, as
9, 21,
45, 93, ...
10-1arithmetic:
Sequences
Functions
are
. When the value of r is halved, the
new terms are
.
59. REASONING If a geometric sequence has a ratio r
such that
, what happens to the terms as n
increases? What would happen to the terms if
?
62. The pattern of filled circles and white circles below
can be described by a relationship between two
variables.
SOLUTION: Sample answer: If a geometric sequence has a ratio
r such that
, as n increases, the absolute value
of the terms will decrease and approach zero
because they are continuously being multiplied by a
fraction. When
, the absolute value of the
terms will increase and approach infinity because
they are continuously being multiplied by a value
greater than 1.
Which rule relates w, the number of white circles, to
f, the number of dark circles?
A
60. WRITING IN MATH Describe what happens to
the terms of a geometric sequence when the
common ratio is doubled. What happens when it is
halved? Explain your reasoning.
B
C
D
SOLUTION: Sample answer: When the value of r is doubled, a 2
SOLUTION: The relation between w and f is
Option C is the correct answer.
doubles, a 3 quadruples, a 4 is multiplied by 8, a5 is
4
multiplied by 2 or 16, and so on. So, the new terms
are
. When the value of r is halved, the
new terms are
.
62. The pattern of filled circles and white circles below
can be described by a relationship between two
variables.
.
64. Find the next term in the geometric
sequence
A
B
C
D
Which rule relates w, the number of white circles, to
f, the number of dark circles?
A
SOLUTION: Find the common ratio.
B
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C
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The common ratio is
.
SOLUTION: relation between
w and f is
10-1The
Sequences
as Functions
Option C is the correct answer.
.
64. Find the next term in the geometric
sequence
A
B
C
D
SOLUTION: Find the common ratio.
The common ratio is
.
The next term in the geometric sequence is
.
Therefore, option D is the correct answer.
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