Question

How many terms of the geometric series $1+4+16+64+...$ will make the sum $5461$?

• A. $6$
• B. $7$
• C. $8$
• D. $9$

Answer 1

Answer: (B)

Let the sum of $n$ terms of the given series is $5461$.
Here, $a=1,r=4$ and $S_n=5461$.
$\Rightarrow a\left(\frac{r^n-1}{r-1}\right)=5461$
$\Rightarrow \frac{4^n-1}{4-1}=5461$
$\Rightarrow 4^n-1=16383$
$\Rightarrow 4^n=16384$
$\Rightarrow 4^n=4^7$
$\Rightarrow n=7$