Question

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

Answer 1

first term $=1$

common ratio $=-a$

$\therefore$ sum $=\frac{\left(1\right)\left(\right(-a{)}^n-1)}{\left(\right(-a)-1)}$

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