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Home  >>  JEEMAIN and NEET  >>  Mathematics  >>  Class11  >>  Sequence and Series

If 20 is divided into four parts which are in AP such that ratio of product of first and fourth part and product of second and third part is 2:3, then the largest part is

$(a)\;6\qquad(b)\;7\qquad(c)\;8\qquad(d)\;9$

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1 Answer

Answer : (c) 8
Explanation : Let the four terms be $\;a-3d\;,a-d\;,a+d\;,and\;a+3d$ with common difference 2d.
$sum=4a=20$
$a=5$
$\frac{(a-3d)(a+3d)}{(a-d)(a+d)}=\frac{2}{3}$
$\frac{25-9d^2}{25-d^2}=\frac{2}{3}$
$d^2=1$
$d=1$
$Largest \;term=a+3d$
$=5+3(1)$
$=8.$
answered Jan 21, 2014 by yamini.v
 

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