Question

If the sum of the geometric series $1+4+16+64+\dots$ is $5461$. Then the number of terms is

Answer 1

Let the required number of terms be $n$.
Here, $a=1,r=4>1$ and $S_n=5461$.
$\therefore S_n=\frac{a(r^n-1)}{(r-1)}$
$\Rightarrow \frac{1\times (4^n-1)}{(4-1)}=5461$
$\Rightarrow (4^n-1)=16383$
$\Rightarrow 4^n=16384=4^7$
$\Rightarrow n=7$
Hence, the required number of terms is $7$.