Sum to indicated number of terms in each of geometric progressions in left.1,-a, a^{2},-a^{3},

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8. Sequences and Series

easy

Find the sum to indicated number of terms in each of the geometric progressions in $\left.1,-a, a^{2},-a^{3}, \ldots n \text { terms (if } a \neq-1\right)$

A

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

B

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

C

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

D

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

Solution

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

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

Common ratio $=r=-a$

$S_{n}=\frac{a_{1}\left(1-r^{n}\right)}{1-r}$

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

Standard 11

Mathematics

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