Chapter 9.1, Problem 10E

To determine

The first five terms of the sequence

Answer to Problem 10E

  $\frac{1}{2},\frac{1}{4},\frac{1}{8},\frac{1}{16},\frac{1}{32}$

Explanation of Solution

Given:

The n^th term is given as

  $a_n={\left(\frac{1}{2}\right)}^n$

Calculation:

Consider that $a_i$ is the i^th term of the sequence

The first five terms of the sequence $a_n={\left(\frac{1}{2}\right)}^n$ can be calculated as

  $\begin{array}{l}{a}_1={\left(\frac{1}{2}\right)}^1=\frac{1}{2}\\ a_2={\left(\frac{1}{2}\right)}^2=\frac{1}{4}\\ a_3={\left(\frac{1}{2}\right)}^3=\frac{1}{8}\\ a_4={\left(\frac{1}{2}\right)}^4=\frac{1}{16}\\ a_5={\left(\frac{1}{2}\right)}^5=\frac{1}{32}\end{array}$

Hence, the first five terms are

  $\frac{1}{2},\frac{1}{4},\frac{1}{8},\frac{1}{16},\frac{1}{32}$