Chapter EP, Problem 11.3.3EP

To determine

To find: The first five terms of series.

Answer to Problem 11.3.3EP

The first five terms of the GP are $0.8,2,5,12.5,31.25$ .

Explanation of Solution

Given: The given sequence is $a_1=0.8,r=2.5$ .

The $n^{th}$ term of a geometric sequence is given by,

$a_n=a_1{r}^{n-1}$

The second term is calculated as

$\begin{array}{c}{a}_2=0.8{\left(2.5\right)}^{2-1}\\ =0.8\left(2.5\right)\\ =2\end{array}$

The third term is calculated as

$\begin{array}{c}{a}_3=0.8{\left(2.5\right)}^{3-1}\\ =5\end{array}$

The fourth term is calculated as

$\begin{array}{c}{a}_4=0.8{\left(2.5\right)}^{4-1}\\ =12.5\end{array}$

The fifth term is calculated as

$\begin{array}{c}{a}_5=0.8{\left(2.5\right)}^{5-1}\\ =31.25\end{array}$

Therefore, the first five terms of the GP are $0.8,2,5,12.5,31.25$ .