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# If in an AP , $\;a_{n}\;$ denotes the $\;n^{th}$ term and $\;a_{p}=\frac{1}{q}$ and $\;a_{q}=\frac{1}{p}$ the root of the equation

$(a)\;a_{p}\qquad(b)\;a_{q}\qquad(c)\;a_{pq}\qquad(d)\;a_{p+q}$

Answer : (c) $\;a_{pq}$
Explanation : Clearly by observation , 1 is root of above equation .
$a_{p}=\large\frac{1}{q}\quad\;a_{q}=\frac{1}{p}$
$a=\large\frac{1}{pq}\quad\;d=\large\frac{1}{pq}$
$1=\large\frac{1}{pq}+(n-1)\;\large\frac{1}{pq}$
$n=pq$
$1\;is\;pq^{th}\;term \;so\;answer\;is\;a_{pq}\;.$