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

Find the sum to n terms in the geometric progression $1,-a, a^{2},-a^{3} \ldots($ if $a \neq-1)$

Solution:

The given G.P. is $1,-a, a^{2},-a^{3}, \ldots \ldots \ldots \ldots . .$

Here, first term $=a_{1}=1$

Common ratio $=r=-a$

$\mathrm{S}_{\mathrm{n}}=\frac{\mathrm{a}_{1}\left(1-\mathrm{r}^{\mathrm{n}}\right)}{1-\mathrm{r}}$

$\therefore S_{n}=\frac{1\left[1-(-a)^{n}\right]}{1-(-a)}=\frac{\left[1-(-a)^{n}\right]}{1+a}$

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