Question

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

Answer 1

$a=1$, $r=4$ and $S_n=341$

$\therefore \frac{a(r^n-1)}{r-1}=341$ or $\frac{1.(4^n-1)}{4-1}=341$

$\therefore 4^n=341\times 3+1=1024=16\times 64=4^5$

$\therefore n=5$