Question

Find the sum of :
$20$ terms of the series $2+6+18+.......$

Answer 1

We have,

$n=20term$

Given series$2+6+18+.....$

Now, first term $a=2$

This series in G.P.

Common ratio$r=\frac{6}{2}=3$

So, $r>1$

Using sum formula of G.P.

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

$S_n=\frac{2(3^{20}-1)}{3-1}$

$S_n=3^{20}-1$

Hence, this is the answer.