Find the sum of n terms in the G.P. x³, x⁵, x⁷, ..... (if x ≠ ± 1)

Solution:

The given G.P is

x³, x⁵, x⁷, .....

Here, a = x³ and r = x²

It is known that

S_n = a (1 - rⁿ)/(1 - r)

Therefore,

S_n = x³ (1 - (x²)ⁿ)/(1 - x²)

= x³ (1 - x²ⁿ)/(1 - x²)

NCERT Solutions Class 11 Maths Chapter 9 Exercise 9.3 Question 10

Find the sum of n terms in the G.P. x³, x⁵, x⁷, ..... (if x ≠ ± 1)

Summary:

We had to find the sum of n terms in the G.P x³, x⁵, x⁷, .... Since we know that S_n = a (1 - rⁿ)/(1 - r) the sum comes out to be x³ (1 - x²ⁿ)/(1 - x²)