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Question

Prove that a,b,c are in A.P., G.P. or H.P. according as the value of abbc is equal to aa,aborac respectively

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Solution

abbc=aagivesb=a+c2inA.P.
abbc=abgivesb2=acinG.P.
abbc=acgivesb=2aca+cinH.P.

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