Question

Find the sum to indicated number of terms in each of the geometric progressions in 1, – a, \(a^2\), –\(a^3\), ... n terms (if a ≠ – 1).

Answer 1

The given G.P. is 1, – a, a2, – a3, ......

Here, first term = a1 = 1

Common ratio = r = a

Sn = \(\frac{a^1(1-r^n)}{1-r}\)

∴Sn = \(\frac{1[1-(-a)^n]}{1-(-a)}\)

= \(\frac{[1-(-a)n]}{1+a}\)