14D –Arithmetic / Geometric Sequences and Series



Arithmetic / Geometric Sequences and Series Name

Identify each sequence below as arithmetic or geometric, the a1 term, and either d (for arithmetic) or r (for geometric).

1. 4, 7, 10, 13, 16 arithmetic or geometric a1=

2. 1, 2, 4, 8, 16, 32 arithmetic or geometric a1=

3. -3, -12, -21, -30, -39 arithmetic or geometric a1=

4. 100, 10, 1, 0.1, 0.01 arithmetic or geometric a1=

5. 4, 20, 100, 500, 2500 arithmetic or geometric a1=

Find the missing term(s) in each arithmetic sequence.

6. 29, _____, -31 7. 32, _____, _____, _____ 68

8. 19, _____, _____ -71 9. [pic], _____, _____, _____, [pic]

Find the missing term(s) in each geometic sequence.

10. -3, _____, -108 11. 3, _____, _____, 648

12. 3125, _____, _____, _____, 5 13. [pic], _____, _____, _____, [pic]

Evaluate each arithmetic series described.

14. [pic] 15. [pic]

16. [pic] 17. [pic]

Evaluate each geometric series described.

18. [pic] 19. [pic]

20. -2 – 6 – 18 – 54 … n = 9 21. [pic]

Determine the number of terms n in each arithmetic series.

22. [pic] 23. [pic]

Determine the number of terms n in each geometric series.

24. [pic] 25. [pic]

26. Determine the seating capacity of an auditorium with 30 rows of seats if there are 20 seats in the first row, 24 seats in the second row, 28 seats in the third and so on.

27. An object with negligible air resistance is dropped from a plane. During the first second of fall, the object falls 4.9 meters; during the second second, it falls 14.7 meters; during the third second, it falls 24.5 meters; during the fourth second, it falls 34.3 meters. If this pattern continues, how many meters will the object fall in 10 seconds?

28. A tool and die company buys a machine for $135,000 and it depreciates at a rate of 30% per year. (In other words, at the end of each year the depreciated value of 70% of what is was at the beginning of the year.) Find the depreciated value of the machine after 5 full years.

29. An investment firm has a job opening with a salary of $30,000 for the first year. Suppose that during the next 39 years, there is a 5%raise each year. Find the total compensation over the 40-year period.

30. The first prize in a contest is $100,000. Each succeeding prize is 75% of the value of the preceding prize. If the number of prizes could be unlimited, find the total amount of money that would be given away.

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