# 13.3E: Geometric Sequences (Exercises)

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13. Find the common ratio for the geometric sequence $$2.5, \quad 5, \quad 10, \quad 20, \ldots$$

14. Is the sequence $$4,16,28,40 \ldots$$ geometric? If so find the common ratio. If not, explain why.

15. A geometric sequence has terms $$a_{7}=16,384$$ and $$a_{9}=262,144 .$$ What are the first five terms?

16. A geometric sequence has the first term $$a_{1}=-3$$ and common ratio $$r=\frac{1}{2} .$$ What is the $$8^{\text {th }}$$ term?

17. What are the first five terms of the geometric sequence $$a_{1}=3, \quad a_{n}=4 \cdot a_{n-1} ?$$

18. Write a recursive formula for the geometric sequence $$1, \quad \frac{1}{3}, \quad \frac{1}{9}, \quad \frac{1}{27}, \ldots$$

19. Write an explicit formula for the geometric sequence $$-\frac{1}{5}, \quad-\frac{1}{15}, \quad-\frac{1}{45}, \quad-\frac{1}{135}, \ldots$$

20. How many terms are in the finite geometric sequence $$-5,-\frac{5}{3},-\frac{5}{9}, \ldots,-\frac{5}{59,049} ?$$

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