10-1 Sequences as Functions Determine whether each sequence is arithmetic. Write yes or no. 1. 8, –2, –12, –22
SOLUTION: Subtract each term from the term directly after it.
The common difference is –10. Therefore, the sequence is arithmetic.
3. 1, 2, 4, 8, 16
SOLUTION: Subtract each term from the term directly after it.
There is no common difference. Therefore, the sequence is not arithmetic.
Find the next four terms of each arithmetic sequence. Then graph the sequence.
5. 6, 18, 30, …
SOLUTION: Subtract each term from the term directly after it.
The common difference is 12. Therefore, the sequence is arithmetic.
To find the next term, add 12 to the last term. 30 + 12 = 42 42 + 12 = 54 54 + 12 = 66 66 + 12 = 78
Graph the sequence.
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There is no common difference. theassequence is not arithmetic. 10-1Therefore, Sequences Functions
Find the next four terms of each arithmetic sequence. Then graph the sequence.
5. 6, 18, 30, …
SOLUTION: Subtract each term from the term directly after it.
The common difference is 12. Therefore, the sequence is arithmetic.
To find the next term, add 12 to the last term. 30 + 12 = 42 42 + 12 = 54 54 + 12 = 66 66 + 12 = 78
Graph the sequence.
7. –19, –11, –3, …
SOLUTION: Subtract each term from the term directly after it.
The common difference is 8. Therefore, the sequence is arithmetic.
To find the next term, add 8 to the last term.
–3 + 8 = 5 5 + 8 = 13 13 + 8 = 21 21 +Manual 8 = 29- Powered by Cognero eSolutions
Graph the sequence.
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10-1 Sequences as Functions 7. –19, –11, –3, …
SOLUTION: Subtract each term from the term directly after it.
The common difference is 8. Therefore, the sequence is arithmetic.
To find the next term, add 8 to the last term.
–3 + 8 = 5 5 + 8 = 13 13 + 8 = 21 21 + 8 = 29
Graph the sequence.
9. FINANCIAL LITERACY Kelly is saving her money to buy a car. She has $250, and she plans to save $75 per week from her job as a waitress.
a. How much will Kelly have saved after 8 weeks?
b. If the car costs $2000, how long will it take her to save enough money at this rate?
SOLUTION: a. Given a 0 = 250, d = 75 and n = 8. After 8 weeks, she will have 250 + (8 × 75) or $850.
b. Given a n = 2000.
Find n.
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So, it will take about 24 weeks to save $2000.
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10-1 Sequences as Functions
9. FINANCIAL LITERACY Kelly is saving her money to buy a car. She has $250, and she plans to save $75 per week from her job as a waitress.
a. How much will Kelly have saved after 8 weeks?
b. If the car costs $2000, how long will it take her to save enough money at this rate?
SOLUTION: a. Given a 0 = 250, d = 75 and n = 8. After 8 weeks, she will have 250 + (8 × 75) or $850.
b. Given a n = 2000.
Find n.
So, it will take about 24 weeks to save $2000.
Determine whether each sequence is geometric. Write yes or no.
11. 4, 12, 36, 108, …
SOLUTION: Find the ratio of the consecutive terms.
Since the ratios are the same, the sequence is geometric.
13. 7, 14, 21, 28, …
SOLUTION: Find the ratio of the consecutive terms.
Since the ratios are not the same, the sequence is not geometric.
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Find the next three terms of each geometric sequence. Then graph the sequence.
15. 8, 16, 32, 64, …
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10-1Since Sequences as are Functions the ratios not the same, the sequence is not geometric.
Find the next three terms of each geometric sequence. Then graph the sequence.
15. 8, 16, 32, 64, …
SOLUTION: Find the ratio of the consecutive terms.
Since the ratios are the same, the sequence is geometric.
To find the next term, multiply the previous term by 2.
Graph the sequence.
17. 9, –3, 1,
,…
SOLUTION: Find the ratio of the consecutive terms.
Since the ratios are the same, the sequence is geometric.
To find the next term, multiply the previous term by
.
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10-1 Sequences as Functions
17. 9, –3, 1,
,…
SOLUTION: Find the ratio of the consecutive terms.
Since the ratios are the same, the sequence is geometric.
To find the next term, multiply the previous term by
.
Graph the sequence.
Determine whether each sequence is arithmetic, geometric, or neither. Explain your reasoning.
19. 200, –100, 50, –25, …
SOLUTION: To find the common difference, subtract any term from the term directly after it.
There is no common difference. Therefore, the sequence is not arithmetic.
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Find the ratio of the consecutive terms.
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10-1 Sequences as Functions
Determine whether each sequence is arithmetic, geometric, or neither. Explain your reasoning.
19. 200, –100, 50, –25, …
SOLUTION: To find the common difference, subtract any term from the term directly after it.
There is no common difference. Therefore, the sequence is not arithmetic.
Find the ratio of the consecutive terms.
The common ratio is
.
Since the ratios are the same, the sequence is geometric.
Determine whether each sequence is arithmetic. Write yes or no.
21.
SOLUTION: Subtract any term from the term directly after it.
There is no common difference. Therefore, the sequence is not arithmetic.
23. 14, –5, –19, …
SOLUTION: Subtract any term from the term directly after it.
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There is no common difference. Therefore, the sequence is not arithmetic. 10-1 Sequences as Functions 23. 14, –5, –19, …
SOLUTION: Subtract any term from the term directly after it.
There is no common difference. Therefore, the sequence is not arithmetic.
Find the next four terms of each arithmetic sequence. Then graph the sequence.
25. –4, –1, 2, 5,…
SOLUTION: Subtract any term from the term directly after it.
The common difference is 3. Therefore, the sequence is arithmetic.
To find the next term, add 3 to the last term.
5+3=8 8 + 3 = 11 11 + 3 = 14 14 + 3 = 17
Graph the sequence.
27. –5, –11, –17, –23, …
SOLUTION: Subtract any term from the term directly after it.
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10-1 Sequences as Functions 27. –5, –11, –17, –23, …
SOLUTION: Subtract any term from the term directly after it.
The common difference is –6. Therefore, the sequence is arithmetic.
To find the next term, add –6 to the last term.
–23 + (–6) = –29 –29 + (–6) = –35 –35 + (–6) = –41 –41 + (–6) = –47
Graph the sequence.
29.
SOLUTION: Subtract any term from the term directly after it.
The common difference is
.
Therefore, the sequence is arithmetic.
To find the- next term, add to the last term. eSolutions Manual Powered by Cognero
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10-1 Sequences as Functions
29.
SOLUTION: Subtract any term from the term directly after it.
The common difference is
.
Therefore, the sequence is arithmetic.
To find the next term, add
to the last term.
Graph the sequence.
31. THEATER There are 28 seats in the front row of a theater. Each successive row contains two more seats than the previous row. If there are 24 rows, how many seats are in the last row of the theater?
SOLUTION: Given a 1 = 28, d = 2 and n = 24.
Find a .
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10-1 Sequences as Functions
31. THEATER There are 28 seats in the front row of a theater. Each successive row contains two more seats than the previous row. If there are 24 rows, how many seats are in the last row of the theater?
SOLUTION: Given a 1 = 28, d = 2 and n = 24.
Find a 24.
Determine whether each sequence is geometric. Write yes or no.
33. 21, 14, 7, …
SOLUTION: Find the ratio of the consecutive terms.
Since the ratios are not the same, the sequence is not geometric.
35. –27, 18, –12, … SOLUTION: Find the ratio of the consecutive terms.
Since the ratios are the same, the sequence is geometric. 37.
SOLUTION: Find the ratio of the consecutive terms.
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SOLUTION: Find the ratio of the consecutive terms. 10-1 Sequences as Functions Since the ratios are the same, the sequence is geometric. 37.
SOLUTION: Find the ratio of the consecutive terms.
Since the ratios are not same, the sequence is not geometric.
Find the next three terms of the sequence. Then graph the sequence.
39. 0.125, –0.5, 2, …
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 with −4.
Graph the sequence.
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the ratios not same, the sequence is not geometric. 10-1Since Sequences as are Functions
Find the next three terms of the sequence. Then graph the sequence.
39. 0.125, –0.5, 2, …
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 with −4.
Graph the sequence.
41. 64, 48, 36, …
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
.
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10-1 Sequences as Functions 41. 64, 48, 36, …
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
.
Graph the sequence.
43.
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 3.
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10-1 Sequences as Functions
43.
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 3.
Graph the sequence.
Determine whether each sequence is arithmetic, geometric, or neither. Explain your reasoning.
45. 3, 12, 27, 48, …
SOLUTION: Subtract each term from the term directly after it.
There is no common difference.
Therefore, the sequence is not arithmetic.
To find the common ratio, find the ratio of the consecutive terms.
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10-1 Sequences as Functions
Determine whether each sequence is arithmetic, geometric, or neither. Explain your reasoning.
45. 3, 12, 27, 48, …
SOLUTION: Subtract each term from the term directly after it.
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.
47. 12, 36, 108, 324, …
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 ratio is 3.
Since the ratios are same, the sequence is geometric.
49.
SOLUTION: Subtract each term from the term directly after it.
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The common ratio is 3.
the ratios same, the sequence is geometric. 10-1Since Sequences as are Functions
49.
SOLUTION: Subtract each term from the term directly after it.
The common difference is
.
Therefore, the sequence is arithmetic.
To find the common ratio, find the ratio of the consecutive terms.
Since the ratios are not same, the sequence is not geometric.
51. READING Sareeta took an 800-page book on vacation. If she was already on page 112 and is going to be on vacation for 8 days, what is the minimum number of pages she needs to read per day to finish the book by the end of her vacation?
SOLUTION: The number of pages to be read is 800 – 112 or 688.
The minimum number of pages to read per day is
.
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?
SOLUTION: Given a 0 = 0.1, n = 37 and r = 2.
Find a 37.
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The minimum number of pages to read per day is
.
10-1 Sequences as Functions
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?
SOLUTION: Given a 0 = 0.1, n = 37 and r = 2.
Find a 37.
The thickness would be about 13,744 km.
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.
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: Neither; the sequence is both arithmetic and geometric.
59. REASONING If a geometric sequence has a ratio r such that WhatManual would happenbytoCognero the terms eSolutions - Powered
SOLUTION:
if
?
, what happens to the terms as n increases? Page 18
SOLUTION: Sample answer: Neither; the sequence is both arithmetic and geometric. 10-1 Sequences as Functions
59. REASONING If a geometric sequence has a ratio r such that What would happen to the terms if
, what happens to the terms as n increases?
?
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.
61. SHORT RESPONSE Mrs. Aguilar’s rectangular bedroom measures 13 feet by 11 feet. She wants to purchase carpet for the bedroom that costs $2.95 per square foot, including tax. How much will it cost to carpet her bedroom?
SOLUTION: 2
The area of the bedroom is 13 × 11 or 143 ft .
It costs $421.85 to carpet the bedroom.
63. SAT/ACT Donna wanted to determine the average of her six test scores. She added the scores correctly to get T, but divided by 7 instead of 6. Her average was 12 less than the actual average. Which equation could be used to determine the value of T?
F
G
H
J
K
SOLUTION: Donna’s average was 12 less than the actual average.
That is,
.
Rewrite the equation.
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Option H is the correct answer.
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costs $421.85 to carpet the bedroom. 10-1ItSequences as Functions
63. SAT/ACT Donna wanted to determine the average of her six test scores. She added the scores correctly to get T, but divided by 7 instead of 6. Her average was 12 less than the actual average. Which equation could be used to determine the value of T?
F
G
H
J
K
SOLUTION: Donna’s average was 12 less than the actual average.
That is,
.
Rewrite the equation.
Option H is the correct answer.
Solve each system of equations.
65.
SOLUTION: Substitute 5 for y in the quadratic equation and solve for x.
The solutions are
.
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67.
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The solutions are . 10-1 Sequences as Functions
67.
SOLUTION: 2
Substitute 3x for y in the second equation and solve for x.
Since the radicand is negative, there is no solution.
Write each equation in standard form. State whether the graph of the equation is a parabola, circle, ellipse, or hyperbola. Then graph the equation.
69.
SOLUTION:
The equation is in the standard form of hyperbola.
Graph each function.
71. eSolutions Manual - Powered by Cognero
SOLUTION:
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10-1 Sequences as Functions Graph each function.
71.
SOLUTION:
The vertical asymptotes are at x = 2 and x = –3.
Since the degree of the numerator is less than the degree of the denominator, the horizontal asymptote is at y = 0.
73.
SOLUTION:
The graph of
is same as the graph of f (x) = x – 6.
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Write an equation of each line.
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10-1 Sequences as Functions
73.
SOLUTION:
The graph of
is same as the graph of f (x) = x – 6.
Write an equation of each line.
75. passes through (6, 4), m = 0.5
SOLUTION: Substitute 0.5, 6 and 4 for m, x1 and y 1 in the point-slope form of a line.
77. passes through (0, –6), m = 3
SOLUTION: Substitute 3, 0 and –6 for m, x1 and y 1 in the point-slope form of a line.
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10-1 Sequences as Functions 77. passes through (0, –6), m = 3
SOLUTION: Substitute 3, 0 and –6 for m, x1 and y 1 in the point-slope form of a line.
79. passes through (1, 3) and
SOLUTION: Find the slope of the line.
Substitute
, 1 and 3 for m, x1 and y 1 in the point-slope form of a line.
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