Question

How many terms of the series $1+4+16+$ .......... make the sum $1,365$?

Answer 1

Here, $a=1,r=\frac{4}{1}=4,S_n=1,365,n=?$
$S_n=\frac{a(r^n-1)}{r-1}$ $[\because r>1]$
$1365=\frac{1[4^n-1]}{4-1}=\frac{4^n-1}{3}$
$1365\times 3=4^n-1$
$4095=4^n-1$
$4096=4^n,4^6=4^n$
$\therefore n=6$