Question

How many terms of the series $1,4,16,...$ must be taken to have their sum equal to $341$?

Answer 1

Given sequence is in G.P with $a=1,r=4$
and $S_n=341$
$\therefore \frac{a(r^n-1)}{r-1}=341or\frac{1.(4^n-1)}{4-1}=341\therefore 4^n=341\times 3+1=1024=16\times 64=4^5$
$\therefore n=5$