Question

A geometric series consists of four terms and has a positive common ratio. The sum of the first two terms is 8 and the sum of the last two terms is $72$. Find the series

Answer 1

Let the sum of the four terms of the geometric series be $a+ar+a{r}^2+a{r}^3$ and $r>0$
Given that $a+ar=8$ and $a{r}^2+a{r}^3=72$
Now, $a{r}^2+a{r}^3=r^2(a+ar)=72$
$\Rightarrow r^2\left(8\right)=72\therefore r=\pm 3$
Since $r>0$, we have $r=3$.
Now, $a+ar=8\Rightarrow a=2$
Thus, the geometric series is $2+6+18+54$.