IF X,Y,Z ARE IN H.P.;Y,Z,T ARE IN G.P. AND Z,T,S ARE IN A.P THEN S=

(xy^2) /(2x-y)^2

x,y,z in hp  so y=2xz/x+z

z=xy/(2x-y)  ........(1)

y,z,t r in gp so  z^2=ty

t=z^2/y

from eqn 1

t=x^2y/(2x-y)^2  ........(2)

z,t,s r in ap so  t=(z+s)/2

s=2t-z

by putting the value of z, t  from eqn 1 &2 

s=[2x^2y-xy(2x-y)]/(2x-y)^2

=[2x^2y-2x^2y+xy^2]/(2x-y)^2

xy^2/(2x-y)^2

okkk i thnk u got ur ans