Question

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

Answer 1

3, 6, 12, .... n 381

$a=3,r=\frac{6}{3}=2,n=?S_n=381$

We know that

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

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

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

$127=2^n-1$

$128=2^n$

$2^7=2^n$

$n=7$