Question

The sum of the first three terms of a geometric progression is $31$ and the sum of the first and the third term is $26$. Find the seventh term of the progression.

Answer 1

given $a+ar+a{r}^2=31$ and $a+a{r}^2=26⟹ar=5$

$a+5r=26⟹5/r+5r=26⟹5r^2-26r+5=0⟹r=5,a=1$

seventh term $A_7={1.5}^6=15625$