Question

The sum of $n$ terms of the $G.P.3,6,12,...$ is $381$. Find the value of $n$

Answer 1

$a=3$

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

Sum$=381$

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

$=381=\frac{3(2^n-1)}{3-1}$

$=\frac{381}{3}=2^n-1$

$=127=2^n-1$

$=128=2^n$

$n=7$.