Question

How many terms of G.P $3,3^2,3^3,...$ are needed to give the sum $120$?

Answer 1

Given G.P is $3,3^2,3^3,..........$
Here first term, $a=3$ and common ratio, $r=3$
Let sum of $n$ terms of given G.P. will give $120$.
$\Rightarrow \frac{a(r^n-1)}{r-1}=\frac{3(3^n-1)}{3-1}=120$
$\Rightarrow 3(3^n-1)=240\Rightarrow 3^n-1=80$
$\Rightarrow 3^n=81=3^4\therefore n=4$
Hence four terms required to give sum of $120$ for given G.P.