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Q 31.

Expert-verified
Found in: Page 809

### Precalculus Enhanced with Graphing Utilities

Book edition 6th
Author(s) Sullivan
Pages 1200 pages
ISBN 9780321795465

# In Problems 29–36, the given pattern continues. Write down the nth term of a sequence $\left\{{a}_{n}\right\}$suggested by the pattern.$1,\frac{1}{2},\frac{1}{4},\frac{1}{8},...$

The nth term of the given sequence is ${a}_{n}=\frac{1}{{2}^{n-1}}$.

See the step by step solution

## Step 1. Write the given information.

The given sequence is:

$1,\frac{1}{2},\frac{1}{4},\frac{1}{8},...$

## Step 2. Determine the pattern of the sequence and write down the nth term.

${a}_{1}=1,{a}_{2}=\frac{1}{2},{a}_{3}=\frac{1}{4},{a}_{4}=\frac{1}{8}$

The pattern of the sequence is:

${a}_{1}=\frac{1}{{2}^{1}-1}=1\phantom{\rule{0ex}{0ex}}{a}_{2}=\frac{1}{{2}^{2-1}}=\frac{1}{2}\phantom{\rule{0ex}{0ex}}{a}_{3}=\frac{1}{{2}^{3-1}}=\frac{1}{4}\phantom{\rule{0ex}{0ex}}{a}_{4}=\frac{1}{{2}^{4-1}}=\frac{1}{8}\phantom{\rule{0ex}{0ex}}{a}_{n}=\frac{1}{{2}^{n-1}}$