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Home  >>  JEEMAIN and AIPMT  >>  Mathematics  >>  Class11  >>  Sequence and Series
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For $\;n \in N \;n \geq 25$ , Let A.G.H be A.M ,G.M and H.M of 25 and n . what is the least value of n such that A.G.H are all natural numbers greater than 25 .

$(a)\;49\qquad(b)\;81\qquad(c)\;169\qquad(d)\;225$

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1 Answer

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Answer : (d) 225
Explanation : $\;A=\large\frac{25+n}{2}$
$G=\sqrt{25n}=5\;\sqrt{n}$
$H=\large\frac{50n}{25+n}$
For A to be natural , n must be odd
For G to be natural n must be a square
Now H wii be natural number
Only if n=225 (All other choices fails).
answered Jan 22, 2014 by yamini.v
 

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