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Q 24.

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Found in: Page 808

### Precalculus Enhanced with Graphing Utilities

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

# In Problems 17–28, write down the first five terms of each sequence.$\left\{{s}_{n}\right\}=\left\{{\left(\frac{4}{3}\right)}^{n}\right\}$

The first five terms of the given sequence are $\frac{4}{3},\frac{16}{9},\frac{64}{27},\frac{256}{81},\frac{1024}{243}$

See the step by step solution

## Step 1. Write the given sequence.

The given sequence is $\left\{{s}_{n}\right\}=\left\{{\left(\frac{4}{3}\right)}^{n}\right\}$

## Step 2. Find the five terms.

To find the five terms in the sequence we substitute $1,2,3,4and5into5$

$\left\{{s}_{1}\right\}=\left\{{\left(\frac{4}{3}\right)}^{1}\right\}=\frac{4}{3}\phantom{\rule{0ex}{0ex}}\left\{{s}_{2}\right\}=\left\{{\left(\frac{4}{3}\right)}^{2}\right\}=\frac{16}{9}\phantom{\rule{0ex}{0ex}}\left\{{s}_{3}\right\}=\left\{{\left(\frac{4}{3}\right)}^{3}\right\}=\frac{64}{27}\phantom{\rule{0ex}{0ex}}\left\{{s}_{4}\right\}=\left\{{\left(\frac{4}{3}\right)}^{4}\right\}=\frac{256}{81}\phantom{\rule{0ex}{0ex}}\left\{{s}_{5}\right\}=\left\{{\left(\frac{4}{3}\right)}^{5}\right\}=\frac{1024}{243}$