Find the sum to n terms in the geometric progression
Question:

Find the sum to n terms in the geometric progression $x^{3}, x^{5}, x^{7} \ldots($ if $x \neq \pm 1)$

Solution:

The given G.P. is $x^{3}, x^{5}, x^{7}, \ldots$

Here, $a=x^{3}$ and $r=x^{2}$

$S_{n}=\frac{a\left(1-r^{n}\right)}{1-r}=\frac{x^{3}\left[1-\left(x^{2}\right)^{n}\right]}{1-x^{2}}=\frac{x^{3}\left(1-x^{2 n}\right)}{1-x^{2}}$