9 Mid-Chapter Quiz

Do you know HOW?

Find the first five terms of each sequence.

1. a n = 3 n + 1 eh sub n , equals , 3 n plus 1
2. a n = − 2 n − 1 eh sub n , equals negative 2 n minus 1
3. a n = n 2 + 2 n eh sub n , equals . n squared , plus 2 n
4. a n = 3 a n − 1 , eh sub n , equals . 3 eh sub n minus 1 end sub . comma  where a 1 = 2 eh sub 1 , equals 2
5. a n = 5 − a n − 1 , eh sub n , equals 5 minus . eh sub n minus 1 end sub . comma  where a 1 = 1 eh sub 1 , equals 1
6. a n = a n − 1 + 2 n , eh sub n , equals . eh sub n minus 1 end sub . plus 2 n . comma  where a 1 = 1 eh sub 1 , equals 1

Write a recursive definition for each sequence.

7. 2 , − 4 , 8 , − 16 , … 2 comma negative 4 comma . 8 comma . negative 16 comma dot dot dot
8. 1, 4, 7, 10, …
9. 4, 2, 5, 1, 6, …

Write an explicit formula for each sequence.

10. 2, 4, 8, 16, …
11. 5 , 2 , − 1 , − 4 , … 5 comma 2 comma negative 1 comma . negative 4 comma dot dot dot
12. 2, 5, 10, 17, …

Find the ninth and tenth terms of each arithmetic sequence.

13. 1, 8, 15, 22, …
14. 4, 10, 16, 22, …
15. 6 , 3 , 0 , − 3 , … 6 comma 3 comma 0 comma negative 3 comma dot dot dot

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

16. 1, 3, 9, 27, …
17. 11, 22, 33, 44, …
18. 1 , − 1 , − 3 , − 5 , − 7 , … 1 comma negative 1 comma . negative 3 comma . negative 5 comma . negative 7 comma dot dot dot
19. 0, 2, 5, 9, 14, …

Find the missing term of each arithmetic sequence.

20. … , 3 , □ , 17 , … dot dot dot comma 3 comma white square comma 17 comma dot dot dot
21. … , 25 , □ , − 15 , … dot dot dot comma 25 comma white square comma negative 15 comma dot dot dot
22. … , − 3 , □ , 8 , … dot dot dot comma negative 3 comma white square comma 8 comma dot dot dot
23. … , 66 , □ , 48 , … dot dot dot comma 66 comma white square comma 48 comma dot dot dot

Find the missing terms of each arithmetic sequence.

24. 4 , a 2 , a 3 , a 4 , 32 , … 4 comma , eh sub 2 , comma . eh sub 3 , comma . eh sub 4 , comma 32 comma dot dot dot
25. 10 , a 2 , a 3 , a 4 , − 20 , … 10 comma , eh sub 2 , comma . eh sub 3 , comma . eh sub 4 , comma . negative 20 comma dot dot dot
26. 5 , a 2 , a 3 , a 4 , 35 , … 5 comma , eh sub 2 , comma . eh sub 3 , comma . eh sub 4 , comma 35 comma dot dot dot

Do you UNDERSTAND?

27. Open-Ended Write the first four terms of an arithmetic sequence with a common difference of 3 and a third term of 10. Then write both a recursive definition and an explicit formula for this sequence.
28. Investments You invested money in a fund and each month you receive a payment for your investment. Over the first four months, you received $50, $52, $55, and $59. If this pattern continues, how much will you receive in the tenth month?
    1. Write a formula to describe this sequence.
    2. Identify your formula as explicit or recursive.
    3. Writing Explain the difference between an explicit formula and a recursive formula. Use your formula from part (a) as part of your explanation.
29. Open-Ended Write the first five terms of a sequence that is not an arithmetic sequence. Then give both an explicit and recursive formula to describe this sequence.
30. Sports A tennis club charges players a $20 court fee plus a $10 hourly charge with a 5-hour maximum. A posted list of the total charges for 1, 2, 3, 4, or 5 hours forms an arithmetic sequence. What is the first term and what is the common difference?

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