How many terms of GP `3,3^2,3^3,`..... are needed to give the sum 120?

Explanation

Let the number of terms be `n`. Then `S_n=120` ( Here `a=3, r=3` )

`rarr a(r^n-1)/r-1=120 rarr 3 (3^n-1)/2=120 rarr 3^n-1=120 xx 2/3 rarr 3^n=80+r=81`

`rarr 3^n=3^4 rarr n=4`