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Home  >>  JEEMAIN and AIPMT  >>  Mathematics  >>  Class11  >>  Sequence and Series
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If in an AP , $\;m^{th}$ term is $\;\frac{1}{n}$ and $\;n^{th}\;term\;is\frac{1}{m}$ , then $\;mn^{th}$ term is :

$(a)\;\frac{1}{mn}\qquad(b)\;\frac{1}{m+n}\qquad(c)\;\frac{1}{m}+\frac{1}{n}\qquad(d)\;1$

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1 Answer

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Answer : (d) 1
Explanation : $a_{m}-a_{n}=\frac{1}{n}-\frac{1}{m}$
$(m-n)\;d=\frac{m-n}{mn}\quad\;d=\frac{1}{mn}$
$a_{mn}-a_{m}=(mn-m)\;d$
$=(mn-m)\;\frac{1}{mn}$
$=\frac{n-1}{n}$
$a_{mn}=\frac{n-1}{n}+\frac{1}{n}=1.$
answered Jan 20, 2014 by yamini.v
 

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