Chapter 8.1, Problem 10E

To determine

To write: the first five terms of the sequence.

Answer to Problem 10E

Five terms of this sequence are $\frac{1}{2},\frac{1}{4},\frac{1}{8},\frac{1}{16},\frac{1}{32}$ respectively.

Explanation of Solution

Given information:

Given sequence

  $a_n={\left(\frac{1}{2}\right)}^n$

Calculation:

Consider the following general term of a sequence,

  $a_n={\left(\frac{1}{2}\right)}^n$

Find the first, second and so on by substituting $n$ as 1,2,and so on. The very first term of the sequence is obtained by putting $n=1$ ,

  $\begin{array}{c}{a}_1={\left(\frac{1}{2}\right)}^1\\ =\frac{1}{2}\end{array}$

For the second term put $n=2$ ,

  $\begin{array}{c}{a}_2={\left(\frac{1}{2}\right)}^2\\ =\frac{1}{4}\end{array}$

For the third term put $n=3$ ,

  $\begin{array}{c}{a}_3={\left(\frac{1}{2}\right)}^3\\ =\frac{1}{8}\end{array}$

For the fourth term put $n=4$

  $\begin{array}{c}{a}_3={\left(\frac{1}{2}\right)}^4\\ =\frac{1}{16}\end{array}$

For fifth term put $n=5$

  $\begin{array}{c}{a}_3={\left(\frac{1}{2}\right)}^5\\ =\frac{1}{32}\end{array}$

The first five terms of the sequence $a_n={\left(\frac{1}{2}\right)}^n$ are $\frac{1}{2},\frac{1}{4},\frac{1}{8},\frac{1}{16},\frac{1}{32}$ .