How many terms of the G.P 3, 3², 3³, .... are needed to give the sum 120?

Solution:

The given G.P is 3, 3², 3³,...

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 (3ⁿ - 1)/(3 - 1)

= 3 (3ⁿ - 1)/2 = 120

⇒ (120 x 2)/3 = 3n - 1

⇒ 3ⁿ - 1 = 80

⇒ 3ⁿ = 81

⇒ 3ⁿ = 3⁴

⇒ n = 4

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

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NCERT Solutions Class 11 Maths Chapter 9 Exercise 9.3 Question 13

How many terms of the G.P 3, 3², 3³, .... 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