1. Tardigrade
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  4. If the sum of n terms of a GP. (with common ratio r) beginning with the p text th term is k times the sum of an equal number of terms of the same series beginning with the q text th term, then the value of k is :

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Q. If the sum of $n$ terms of a GP. (with common ratio r) beginning with the $p^{\text {th }}$ term is $k$ times the sum of an equal number of terms of the same series beginning with the $q ^{\text {th }}$ term, then the value of $k$ is :

Sequences and Series

Solution:

$ \frac{ a _{ p }\left( r ^{ n }-1\right)}{ r -1}=\frac{ ka _{ q }\left( r ^{ n }-1\right)}{ r -1} $
$\text { a } r ^{ p ^{-1}}= k \cdot a r ^{ q -1}$
$ k = r ^{ p - q }$