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

**Solution:**

The given G.P is 3, 3^{2}, 3^{3},...

Let n terms of this G.P be required to obtain a sum as 120.

Here, a = 3 and r = 3

Therefore,

S_{n} = 3 (3^{n} - 1)/(3 - 1)

= 3 (3^{n} - 1)/2 = 120

⇒ (120 x 2)/3 = 3n - 1

⇒ 3^{n} - 1 = 80

⇒ 3^{n} = 81

⇒ 3^{n} = 3^{4}

⇒ n = 4

Thus, four terms of the given G.P are required to obtain the sum of 120

NCERT Solutions Class 11 Maths Chapter 9 Exercise 9.3 Question 13

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

**Summary:**

The given series was 3, 3^2, 3^3, .... which is G.P, and the total terms required need to get the sum 120 is 4