Chapter 8.1, Problem 23E

Working with sequences Several terms of a sequence ${\{a_n\}}_{n=1}^{\infty }$ are given.

1. a. Find the next two terms of the sequence.
2. b. Find a recurrence relation that generates the sequence (supply the initial value of the index and the first term of the sequence).
3. c. Find an explicit formula for the nth term of the sequence.

23. $\left\{1,\frac{1}{2},\frac{1}{4},\frac{1}{8},\frac{1}{16},\dots \right\}$