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Q.
If the $n$th term of the geometric progression, $5,-\frac{5}{2}, \frac{5}{4},-\frac{5}{8}, \ldots$ is $\frac{5}{1024}$, then the value of $n$ is
ManipalManipal 2017
Solution:
According to the question,
$5\left(-\frac{1}{2}\right)^{n-1}=\frac{5}{1024}$
$\Rightarrow\left(-\frac{1}{2}\right)^{n-1}=\left(\frac{1}{2}\right)^{10}$
$\Rightarrow n-1=10$
$\Rightarrow n=11$