Find the sum to indicated number of terms in each of the geometric progressions in 1, – a, a 2 , – a, ... n terms (if a – 1).

Question

Philoid · Accepted Answer

Given: 1, – a, a², – a, ... n terms

Sum of n terms of a G.P. is given by: (a: First term of G.P, r: common difference of G.P, n: Number of terms of the G.P)

First term of the Given G.P (a) = 1

Common difference of the given G.P(r) = = -a

Number of terms(n): n

Let the sum of n terms be s

∴ s =

⇒ s =

⇒ s = [

∴ The sum of n terms of the given sequence is: [1-(-a)ⁿ]