Chapter 12.1, Problem 24AYU

In Problems 17-28, write down the first five terms of each sequence.

$\left\{s_n\right\}\text{ = }\left\{{\left(\frac{4}{3}\right)}^n\right\}$

To determine

To find: The first five terms of each sequence.

Answer to Problem 24AYU

$\{s_1\}=\frac{4}{3},\{s_2\}=\frac{16}{9},\{s_3\}=\frac{64}{27},\{s_4\}=\frac{256}{81}, \{s_5\}=\frac{1024}{243}$

Explanation of Solution

Given:

$\{s_n\}=\left\{{\left(\frac{4}{3}\right)}^n\right\}$

Calculation:

Let $n=1,2,3,4,5$

$\{s_n\}=\left\{{\left(\frac{4}{3}\right)}^n\right\}$

$\{s_1\}=\left\{{\left(\frac{4}{3}\right)}^1\right\}=\frac{4}{3}$

$\{s_2\}=\left\{{\left(\frac{4}{3}\right)}^2\right\}=\frac{16}{9}$

$\{s_3\}=\left\{{\left(\frac{4}{3}\right)}^3\right\}=\frac{64}{27}$

$\{s_4\}=\left\{{\left(\frac{4}{3}\right)}^4\right\}=\frac{256}{81}$

$\{s_5\}=\left\{{\left(\frac{4}{3}\right)}^5\right\}=\frac{1024}{243}$