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 :

Question

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 : (A) r p / q  (B) rq / p (C) rp-q (D) rp+q

Tardigrade Admin · Accepted Answer

( a p ( r n -1)/ r -1)=( ka q ( r n -1)/ r -1) text a r p -1= k ⋅ a r q -1 k = r p - q

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

$r^{p / q}$

$r^{q / p}$

$r^{p - q}$

$r^{p + q}$

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

Q. If the sum of n terms of a GP. (with common ratio r) beginning with the pth term is k times the sum of an equal number of terms of the same series beginning with the qth term, then the value of k is :

rp/q

rq/p

rp−q

rp+q