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 = $\frac{1[1-(-a)^n]}{1-(-a)}$

= $\frac{[1-(-a)n]}{1+a}$