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 \(-5,-\frac{5}{3},-\frac{5}{9}, \ldots,-\frac{5}{59,049} ?\)