Determine whether each sequence is arithmetic 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. ANSWER: Yes 2. –19 , –12 , –5 , 2 , 9 SOLUTION: Subtract each term from the term directly after it. The common difference is 7. Therefore, the sequence is arithmetic. ANSWER: Yes 3. 1 , 2 , 4 , 8 , 16 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. ANSWER: No 4. 0.6 , 0.9 , 1.2 , 1.8, ... SOLUTION: Subtract each term from the term directly after it. There is no common difference. Therefore, the sequence is not arithmetic. ANSWER: No Find the next four terms of each arithmetic eSolutions Manual - Powered by Cognero Page 1 10 - 1 Sequences as Functions
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Determine whether each sequence is arithmeticno.
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.
ANSWER:Yes
2.19, 12, 5, 2, 9
SOLUTION:Subtract each term from the term directly after it.
The common difference is 7. Therefore, the sequence is arithmetic.
ANSWER:Yes
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.
ANSWER:No
4.0.6, 0.9, 1.2, 1.8, ...
SOLUTION:Subtract each term from the term directly after it.
There is no common difference. Therefore, the sequence is not arithmetic.
ANSWER:No
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.
ANSWER:42, 54, 66, 78
6.15, 6, 3,
SOLUTION:Subtract each term from the term directly after it.
The common difference is 9. Therefore, the sequence is arithmetic. To find the next term, add 9 to the last term. 3 + (9) = 12 12 + (9) = 21 21 + (9) = 30 30 + (9) = 39 Graph the sequence.
ANSWER:12, 21, 30, 39
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.
ANSWER:5, 13, 21, 29
8.26, 33, 40,
SOLUTION:Subtract each term from the term directly after it.
The common difference is 7. Therefore, the sequence is arithmetic. To find the next term, add 7 to the last term. 40 + (7) = 47 47 + (7) = 54 54 + (7) = 61 61 + (7) = 68 Graph the sequence.
ANSWER:47, 54, 61, 68
9.FINANCIALLITERACYKelly 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 a0 = 250, d = 75 and n = 8.
After 8 weeks, she will have 250 + (8 75) or $850. b. Given an = 2000.
Find n.
So, it will take about 24 weeks to save $2000.
ANSWER:a. $850 b. 24 wk
Determine whether each sequence is geometric. Write yes or no.
10.8, 5, 1, 4,
SOLUTION:Find the ratio of the consecutive terms.
Since the ratios are not same, the sequence is not geometric.
ANSWER:No
11.4, 12, 36, 108,
SOLUTION:Find the ratio of the consecutive terms.
Since the ratios are the same, the sequence is geometric.
ANSWER:Yes
12.27, 9, 3, 1,
SOLUTION:Find the ratio of the consecutive terms.
Since the ratios are the same, the sequence is geometric.
ANSWER:Yes
13.7, 14, 21, 28,
SOLUTION:Find the ratio of the consecutive terms.
Since the ratios are not the same, the sequence is notgeometric.
ANSWER:No
Find the next three terms of each geometric sequence. Then graph the sequence.
14.8, 12, 18, 27,
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.
ANSWER:40.5, 60.75, 91.125
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.
ANSWER:128, 256, 512
16.250, 50, 10, 2,
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.
ANSWER:
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.
ANSWER:
Determine whether each sequence is arithmetic, geometric, or neither. Explain your reasoning.
18.5, 1, 7, 3, 9,
SOLUTION:
There is no common difference. Therefore, the sequence is not arithmetic. Find the ratio of the consecutive terms.
Since the ratios are not the same, the sequence is notgeometric.
ANSWER:Neither; there is no common difference or ratio.
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.
ANSWER:
Geometric; the common ratio is .
20.12, 16, 20, 24,
SOLUTION:To find the common difference, subtract any term from the term directly after it.
The common difference is 4. Therefore, the sequence is arithmetic. Find the ratio of the consecutive terms.
Since the ratios are not the same, the sequence is notgeometric.
ANSWER:Arithmetic; the common difference is 4.
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.
ANSWER:No
22.9, 3, 0, 3, 9
SOLUTION:Subtract any term from the term directly after it.
There is no common difference. Therefore, the sequence is not arithmetic.
ANSWER:No
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.
ANSWER:No
24.
SOLUTION:Subtract any term from the term directly after it.
The common difference is .
Therefore, the sequence is arithmetic.
ANSWER:Yes
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.
ANSWER:8, 11, 14, 17
26.10, 2, 6, 14,
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. 14 + (8) = 22 22 + (8) = 30 30 + (8) = 38 38 + (8) = 46 Graph the sequence.
ANSWER:22, 30, 38, 46
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.
ANSWER:29, 35, 41, 47
28.19, 2, 15,
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 Graph the sequence.
ANSWER:32, 49, 66, 83
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 tothelastterm.
Graph the sequence.
ANSWER:
30.
SOLUTION:Subtract any term from the term directly after it.
The common difference is 1. Therefore, the sequence is arithmetic. To find the next term, add 1 to the last term.
Graph the sequence.
ANSWER:
31.THEATER There are 28 seats in the front row of atheater. 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 a1 = 28, d = 2 and n = 24.
Find a24.
ANSWER:74
32.CCSS SENSE-MAKINGMario began an exerciseprogram 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. Is it reasonable for this pattern to continue indefinitely? Explain.
SOLUTION:a. Given a1 = 5, d = 1.5 and n = 18.
Find a18.
Therefore he will row for 30 minutes and 30 secondson the 38th day. b. Given a1 = 5, d = 1.5 and an = 60.
Find n.
Mario will first row an hour or more on the 38th day. c. Sample answer: It is unreasonable because there are only so many hours in the day that can be dedicated to rowing.
ANSWER:a. 30 minutes and 30 seconds b. on the 38th day 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.
33.21, 14, 7,
SOLUTION:Find the ratio of the consecutive terms.
Since the r
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