Question

Find the first term of a G.P. in which $S_8=510$ and $r=2$.

Answer 1

We know that the formula for sum of $n$ terms of G.P is $S_n=\frac{a(r^n-1)}{r-1}$, where $a$ is the first term, $r$ is the common ratio.

It is given that the $8$th term of a G.P is $S_8=510$, the common ratio is $r=2$ and the number of terms are $n=8$, therefore,

$S_n=\frac{a(r^n-1)}{r-1}\Rightarrow S_8=\frac{a(2^8-1)}{2-1}\Rightarrow 510=\frac{a(256-1)}{1}\Rightarrow 510=255a\Rightarrow a=\frac{510}{255}=2$

Hence, the first term is $2$.