The sum of some terms of G.P. is 315 whose first term and the common ratio are 5 and 2,

Let the sum of n terms of the G.P. be 315.

It is known that, $\mathrm{S}_{n}=\frac{a\left(r^{n}-1\right)}{r-1}$

It is given that the first term $a$ is 5 and common ratio $r$ is 2 .

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

$\Rightarrow 2^{n}-1=63$

$\Rightarrow 2^{n}=64=(2)^{6}$

$\Rightarrow n=6$

$\therefore$ Last term of the G.P $=6^{\text {th }}$ term $=a r^{6-1}=(5)(2)^{5}=(5)(32)=160$

Thus, the last term of the G.P. is 160 .