13.3E: Geometric Sequences (Exercises)

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Dec 26, 2024
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- 13.3: Geometric Sequences
- 13.4: Series and Their Notations

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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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