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 \(12,20,28, \ldots, 172 ?\)