Chapter 8, Problem 7RE

To determine

To find: first five terms of the sequence.

Answer to Problem 7RE

First five terms of the sequence are $9,3,1,\frac{1}{3},\frac{1}{9}$ respectively.

Explanation of Solution

Given information:

An sequence is given with first term WA $a_1=9$ and a recurrence relation $a_{k+1}=\frac{1}{3}{a}_k$ .

Calculation:

Now, consider the first term.

  $a_1=9$

And

  $a_{k+1}=\frac{1}{3}{a}_k$

First five terms of the sequence can be found by substituting 1, 2, 3, 4, and 5 for kas shown:

  $\begin{array}{l}{a}_2=\frac{1}{3}{a}_1=\frac{1}{3}\times 9=3\\ a_3=\frac{1}{3}{a}_2=\frac{1}{3}\times 3=1\\ a_4=\frac{1}{3}{a}_3=\frac{1}{3}\times 1=\frac{1}{3}\\ a_5=\frac{1}{3}{a}_4=\frac{1}{3}\times \frac{1}{3}=\frac{1}{9}\end{array}$

Hence, the first five terms of the sequence are $9,3,1,\frac{1}{3},\frac{1}{9}$ respectively.