Chapter 12, Problem 18SGA

To determine

To find: the first term of the geometric sequence.

Answer to Problem 18SGA

125000

Explanation of Solution

Given information:

  $\begin{array}{l}{a}_7=8\\ r=0.2\\ n=7\end{array}$

Calculation:

The first term $\left(a_1\right)$ of the geometric sequence can be evaluated as shown below.

  $\begin{array}{c}{a}_n=a_1{r}^{n-1}\\ a_7=a_1{r}^{7-1}\left[\text{Put }n=7\right]\\ a_7=a_1{r}^6\\ 8=a_1{\left(0.2\right)}^6\left[\text{Put the value of }{a}_7\text{ and }r\right]\\ a_1=\frac{8}{{\left(0.2\right)}^6}\\ =\frac{2^3}{2^6{\left(0.1\right)}^6}\\ =\frac{{10}^6}{2^3}\\ =125000\end{array}$

Thus first term of the geometric sequence is 125000.