# 13.2E: Arithmetic Sequences (Exercises)

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5. Is the sequence $$\frac{4}{7}, \frac{47}{21}, \frac{82}{21}, \frac{39}{7}, \ldots$$ arithmetic? If so, find the common difference.

6. Is the sequence $$2,4,8,16, \quad \ldots$$ arithmetic? If so, find the common difference.

7. An arithmetic sequence has the first term $$a_{1}=18$$ and common difference $$d=-8 .$$ What are the first five terms?

8. An arithmetic sequence has terms $$a_{3}=11.7$$ and $$a_{8}=-14.6 .$$ What is the first term?

9. Write a recursive formula for the arithmetic sequence $$-20,-10,0,10, \ldots$$

10. Write a recursive formula for the arithmetic sequence $$0, \quad-\frac{1}{2}, \quad-1, \quad-\frac{3}{2}, \ldots,$$ and then find the $$31^{\text {st }}$$ term.

11. Write an explicit formula for the arithmetic sequence $$\frac{7}{8}, \quad \frac{29}{24}, \quad \frac{37}{24}, \quad \frac{15}{8}, \ldots$$

12. How many terms are in the finite arithmetic sequence $$12,20,28, \ldots, 172 ?$$

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