Practice and Problem-Solving Exercises

A Practice

See Problem 1.

Determine whether each sequence is arithmetic. If so, identify the common difference.

7. 10, 20, 30, 40, …
8. 1, 1, 2, 3, 5, 8, …
9. − 21 , − 18 , − 15 , − 12 , … negative 21 comma negative 18 comma . negative 15 comma . negative 12 comma dot dot dot
10. 97, 86, 75, 64, …
11. 3, 7, 11, 15, …
12. 100, 10, 1, 0.1, …

See Problem 2.

Find the 32nd term of each sequence.

13. 34, 37, 40, 43, …
14. − 9 , − 8.7 , − 8.4 , … negative 9 comma negative 8.7 comma negative 8.4 comma dot dot dot
15. 23, 30, 37, 44, …
16. 9 , 4 , − 1 , − 6 , − 11 , … 9 comma 4 comma negative 1 comma . negative 6 comma . negative 11 comma dot dot dot
17. 0.1, 0.5, 0.9, 1.3, …
18. 101, 105, 109, 113, …

See Problem 3.

Find the missing term of each arithmetic sequence.

19. − 15 , □ , 1 , … negative 15 comma white square comma 1 comma dot dot dot
20. 14 , □ , 28 , … 14 comma white square comma 28 comma dot dot dot
21. … 5 , □ , 21 , … dot dot dot 5 comma white square comma 21 comma dot dot dot
22. … 98 , □ , 66 , … dot dot dot 98 comma white square comma 66 comma dot dot dot
23. 25 , □ , − 10 , … 25 comma white square comma negative 10 comma dot dot dot
24. … 65 , □ , − 60 , … dot dot dot 65 comma white square comma negative 60 comma dot dot dot

See Problem 4.

25. Savings A student deposits the same amount of money into her bank account each week. At the end of the second week she has $30 in her account. At the end of the third week she has $45 in her account. How much will she have in her bank account at the end of the ninth week?

B Apply

Find the 17th term of each sequence.

26. a 16 = 18 , d = 5 eh sub 16 , equals 18 . comma , d equals 5
27. a 16 = 21 , d = − 3 eh sub 16 , equals 21 . comma d equals negative 3
28. a 18 = − 5 , d = 12 eh sub 18 , equals , minus 5 comma , d equals 12
29. a 18 = 32 , d = − 4 eh sub 18 , equals 32 . comma d equals negative 4
30. a 16 = 1 5 , d = 1 2 eh sub 16 , equals , 1 fifth , comma d equals , 1 half
31. a 18 = − 9 , d = − 11 eh sub 18 , equals , minus 9 comma d equals negative 11
32. Think About a Plan The arithmetic mean of the monthly salaries of two employees is $3210. One employee earns $3470 per month. What is the monthly salary of the other employee?
    • What is the given information and what is the unknown?
    • What equation can you use to find the other monthly salary?
33. Error Analysis A student claims that the next term of the arithmetic sequence 0, 2, 4, … is 8. Explain and correct the student's error.

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