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Question

Prove that a,b,c are in G.P., if logan,logbn,logcn are in H.P.

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Solution

logan,logbn,logcn are in H.P.
Taking reciprocals
logna,lognb,lognc are in H.P.
or 2lognb=logna+lognc
or lognb2=lognacb2=ac
Hence a,b,c are in G.P.

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