Question

The sum of some terms of 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 the sum of n terms of G.P. be 315 i.e. $S_n=315$.

Here, a = 15, r = 2

$\therefore S_n=\frac{a(r^n-1)}{r-1}$

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

$\Rightarrow 2^n-1=\frac{315}{5}=63$

$\therefore 2^n=63+1=64=2^6$

$\Rightarrow n=6$

Now, $a_6=5\times 2^6-1=5\times 2^5$

$=5\times 32=160$