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If p^th term of an HP is q and q^th term is p. Then find (p+q)^th term
Option: 1
$\frac{pq}{p+q}$

Option: 2
$\frac{p+q}{pq}$

Option: 3
p+q

Option: 4
Zero

Answers (1)

best_answer

Let a be first term and d be common difference of corresponding AP.

given p^th term of H.P. a_p = q

So p^th term of AP = $\frac{1}{q}$

$a+(p-1)d=\frac{1}{q}$ ........(1)

Similarly,

$a+(q-1)d=\frac{1}{p}$ .......(2)

(1) - (2)

$(p-q)d=\frac{1}{q}-\frac{1}{p}$

$(p-q)d=\frac{p-q}{pq}$

$\Rightarrow d=\frac{1}{pq}$

Using (1)

$a+\frac{p-1}{pq}=\frac{1}{q}$

$a=\frac{1}{pq}$ ........(4)

So (p+q)^th term for AP

$a+(p+q-1)d$

$=\frac{1}{pq}+\frac{(p+q-1)}{pq}$

$=\frac{p+q}{pq}$

$\therefore$ $a_{p+q}$ for HP $= \frac{pq}{p+q}$

Posted by

Rakesh

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