Question

The sum of some terms of a G.P. is $315$, whose first term and the common ratio are $5$ and $2$, respectively. Find the last term and the number of terms.

Answer 1

Let there be n terms in the G.P. with first term $a=5$ and common ratio $r=2$. Then,

Sum of n terms = 315

$a\left(\frac{r^n-1}{r-1}\right)=315$

$5\left(\frac{2^n-1}{2-1}\right)=315$

$2^n-1=63$

$2^n=64$

$n=6$

Therefore, last term = $a{r}^{n-1}=5\times 2^{6-1}=160$