show that A.M (arithmetic mean), G.M and H.M of two positive numbers are in G.P.
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Verified answer
Let a and b two numbersAM=(a+b)/2
GM=√ab
HM=2ab/(a+b)
if we multiply AM.HM
then,
AM.HM=(a+b)/2.{2ab/(a+b)}
=ab=(√ab)^2=GM^2
hence ,
AM.HM=GM^2
AM/GM=GM/HM
we know in geometric progression ratio of two consecutive number always constant .
so,
AM, GM , HM are in GP