9 Chapter Test

Do you know HOW?

Write a recursive definition and an explicit formula for each sequence. Then find a 12 . eh sub 12 , .

1. 7, 13, 19, 25, 31, …
2. 10, 20, 40, 80, 160, …

Determine whether each sequence is arithmetic, geometric, or neither. Then find the tenth term.

3. 23, 27, 31, 35, 39, …
4. − 12 , − 5 , 2 , 9 , 16 , … negative 12 comma , negative 5 comma , 2 comma 9 comma 16 comma dot dot dot
5. − 5 , 15 , − 45 , 135 , − 405 , … negative . 5 comma 15 comma negative 45 comma . 135 comma . negative 405 comma dot dot dot
6. 1 4 , 1 , 4 , 16 , … 1 fourth , comma 1 comma 4 comma 16 comma dot dot dot

Find the missing term of each arithmetic sequence.

7. 4 , □ , 12 , … 4 comma white square comma 12 comma dot dot dot
8. − 11 , □ , 23 , … negative 11 comma white square comma 23 comma dot dot dot

Determine whether each sequence is arithmetic or geometric. Then identify the common difference or common ratio.

9. 1620, 540, 180, 60, 20, …
10. 78, 75, 72, 69, 66, 63, 60, …
11. 3 32 , 3 16 , 3 8 , 3 4 , 3 2 , 3 , 6 , … 3 thirty seconds , comma , 3 sixteenths , comma , 3 eighths , comma , 3 fourths , comma , 3 halves , comma 3 comma 6 comma dot dot dot

a 1 eh sub 1  is the first term of a sequence, r is a common ratio, and d is a common difference. Write the first five terms.

12. a 1 = 2 , r = − 2 eh sub 1 , equals 2 . comma r equals negative 2
13. a 1 = 3 , d = 7 eh sub 1 , equals 3 . comma , d equals 7
14. a 1 = − 100 , r = 1 5 eh sub 1 , equals , minus 100 comma . r equals , 1 fifth
15. a 1 = 19 , d = − 4 eh sub 1 , equals 19 . comma d equals negative 4

Find the missing term of each geometric sequence.

16. 2 , □ , 0 . 5 , … 2 comma white square comma 0 . 5 comma dot dot dot
17. 2 , □ , 8 , … 2 comma white square comma 8 comma dot dot dot

Find the sum of each infinite geometric series.

18. 0 . 5 + 0 . 05 + 0 . 005 + … 0 . 5 plus 0 . 05 plus 0 . 005 plus dot dot dot
19. 1 − 1 2 + 1 4 − … 1 minus , 1 half , plus , 1 fourth , minus dot dot dot
20. 6 + 5 + 25 6 + … 6 plus 5 plus , 25 over 6 , plus dot dot dot

Determine whether each series is arithmetic or geometric. Then evaluate the finite series for the specified term number.

21. 2 + 7 + 12 + … ; n = 8 2 plus 7 plus 12 plus . dot dot dot semicolon , n equals 8
22. 5000 + 1000 + 200 + … ; n = 5 5000 , plus , 1000 , plus 200 plus . dot dot dot semicolon , n equals 5
23. 1 + 0 . 01 − 0 . 98 − … ; n = 5 1 plus 0 . 01 minus 0 . 98 minus dot dot dot semicolon , n equals 5
24. 2 + 6 + 18 + … ; n = 6 2 plus 6 plus 18 plus . dot dot dot semicolon , n equals 6

Find the sum of each series.

25. ∑ n = 1 5 ( 3 n + 1 ) sum , from , n equals 1 , to , 5 , of . open , 3 n plus 1 , close
26. ∑ n = 1 8 2 n 3 sum , from , n equals 1 , to , 8 , of . fraction 2 n , over 3 end fraction
27. ∑ n = 4 10 ( 0.8 n − 0.4 ) sum , from , n equals 4 , to , 10 , of . open . 0.8 n minus 0.4 . close
28. ∑ n = 2 6 ( − 2 ) n − 1 sum , from , n equals 2 , to , 6 , of . open , negative 2 , close super n minus 1 end super

Do you UNDERSTAND?

29. You have saved $50. Each month you add $10 more to your savings.
    1. Write an explicit formula to model the amount you have saved after n months.
    2. How much have you saved after six months?
30. Open-Ended Write an arithmetic sequence. Then write an explicit formula for it.
31. Reasoning How can you tell if a geometric series converges or diverges? Include examples of both types of series. Evaluate the series that converges.
32. A diamond is purchased for $2500. Suppose its value increases 5% each year.
    1. What is the value of diamond after 8 years?
    2. Writing Explain how you can write an explicit formula for a geometric sequence to answer the question.

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