Thank you for reporting, we will resolve it shortly
Q.
How many terms of the geometric series $1 + 4 + 16 + 64 + ...$ will make the sum $5461$?
Sequences and Series
Solution:
Let the sum of $n$ terms of the given series is $5461$.
Here, $a = 1, r = 4$ and $S_n = 5461$.
$ \Rightarrow a\left(\frac{r^{n}-1}{r-1}\right) = 5461$
$ \Rightarrow \frac{4^{n}-1}{4-1} = 5461$
$\Rightarrow 4^{n} -1= 16383$
$\Rightarrow 4^{n} = 16384$
$ \Rightarrow 4^{n } = 4^{7}$
$ \Rightarrow n= 7$