Sequences and Series Practice for Test



Sequences and Series Practice for Test Name ___________________________

1. Find the next four terms of each sequence and write the equation for the nth term.

35, 32, 29, 26, … _____ , _____ , _____ , _____ [pic] = ______________

2. Given the explicit formula for the sequence, find the first five terms and the named term in the problem.

[pic] _____ , _____ , _____ , _____ , _____

[pic] = _________

3. Given the explicit formula for the sequence, find the first five terms and the named term in the problem.

[pic] _____ , _____ , _____ , _____ , _____

[pic] = _________

4. Given the first term and the common difference of an arithmetic sequence find the first five terms and the explicit formula.

[pic] _____ , _____ , _____ , _____ , _____

[pic] = _________

5. Given a term and the common difference of an arithmetic sequence find the first five terms and the explicit formula.

[pic] _____ , _____ , _____ , _____ , _____

[pic] = _________

6. Given the first term and the common ratio of a geometric sequence find the first five terms and the explicit formula.

[pic] _____ , _____ , _____ , _____ , _____

[pic] = _________

7. Given a term and the common ratio of a geometric sequence find the first five terms and the explicit formula.

[pic] _____ , _____ , _____ , _____ , _____

[pic] = _________

8. Evaluate each series.

[pic]

9. Evaluate each series.

[pic]

10. Rewrite each series using sigma notation.

8 + 27 + 64 + 125 + 216

11. Evaluate each arithmetic series.

[pic]

12. Evaluate each arithmetic series.

20 + 27 + 34 + 41 … , n =16

13. Evaluate each geometric series.

[pic]

14. Evaluate each geometric series.

-3 + -6 + -12 + -24 … , n = 9

15. Evaluate each geometric series.

[pic]

16. Edgar is getting better at math. On his first quiz he scored 57 points, then he scores 61 and 65 on his next two quizzes. If his scores continued to increase at the same rate, what will be his score on his 9th quiz? Show all work. (Do not use Kindergarten Method)

17. A house worth $350,000 when purchased was worth $335,000 after the first year and $320,000 after the second year. If the economy does not pick up and this trend continues, what will be the value of the house after 6 years. Show all work. (Do not use Kindergarten Method)

18. A theater has 32 rows of seats. If there are 26 seats in the 1st row, 30 in the 2nd, 34 in the 3rd, and so on, how many seats are there in all?

19. A tube well is bored 800 meters deep. The 1st meter costs $250 and the cost per meter increases by $50 for every subsequent meter. Find the cost of boring the 750th meter and the total cost incurred for the entire job.

20. A culture of bacteria doubles every 2 hours.  If thereare 500 bacteria at the beginning, how many bacteria will there be after 24 hours?

21. A mine worker discovers an ore sample containing 500 mg of radioactive material.  It is discovered that the radioactive material has a half life of 1 day.  Find the amount of radioactive material in the sample at the beginning of the 7th day.

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