Class 11

Math

Algebra

Sequences and Series

How many terms of G.P. $3,3_{2},3_{3},˙˙˙$are needed to give the sum 120?

**Solution: **Solution: In the given GP,

$a=3,r=3$

$S_{n}=120$

$∴ar−1r_{n}−1 =120$

$⇒33−1r_{n}−1 =120$

$⇒3_{n}−1=80⇒3_{n}=81$

$⇒3_{n}=3_{4}$

$n=4$