Chapter 11.3, Problem 55PPS

To determine

Find $a_1$ in a geometric series for which $a_n=1024;n=5;r=8$

Answer to Problem 55PPS

  $a_1=\frac{1}{4}$

Explanation of Solution

Given:

Find $a_1$ in a geometric series for which $a_n=1024;n=5;r=8$

Concept Used:

The general nth term formula for GP series is $a_n=a_1·r^{n-1}$

Calculation:

  $a_n=1024;n=5;r=8;\text{Find}{a}_1$

  $\begin{array}{l}{a}_n=a_1·r^{n-1}\\ 1024=a_1·8^{5-1}\\ 1024=a_1·8^4=4096a_1\\ 1024=4096·a_1\\ \frac{1024}{4096}=\frac{4096·a_1}{4096}\\ a_1=\frac{1}{4}\end{array}$

Thus, $a_1=\frac{1}{4}$