Question

Find the sum to indicate number of terms in each of the geometric progression in
$1,-a,-a^2,-a^3......nterms(ifa\ne -1).$

Answer 1

Here the first term of G.P, = 1, and common ratio = $\frac{-a}{1}=-a$

We know that,

$S_n=\frac{a(1-r^n)}{1-r}$

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

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