Find the sum of n terms in the G.P √7, √21, 3, √7, ....

Solution:

The given G.P is

√7, √21, 3, √7, ....

Here, a = √7 and r = √21/√7 = √3

It is known that S_n = a (1 - rⁿ)/(1 - r)

Therefore,

S_n = √7 (1 - (√3)ⁿ)/(1 - √3)

= [√7 (1 - (√3)ⁿ)/(1 - √3)] x [(1 + √3)/(1 + √3)]

= √7(1 + √3) [(1 - (√3)ⁿ)]/(1 - 3)

= - √7(1 + √3) [(1 - (√3)ⁿ)]/2

= √7(1 + √3)/2 [(3)^n/2 - 1]

NCERT Solutions Class 11 Maths Chapter 9 Exercise 9.3 Question 8

Find the sum of n terms in the G.P √7, √21, 3, √7, ....

Summary:

The sum of n terms in the G.P √7, √21, 3, √7... We have found the sum is √7(1 + √3)/2 [(3)^n/2 - 1]