Q. 175.0( 2 Votes )

# If are three consecutive terms of an A.P., prove that a, b, c are the three consecutive terms of a G.P.

Answer :

Given are in AP.

⇒ {taking arithmetic mean – to get the relationship}

⇒

⇒ ab + ac + b^{2} + bc = b^{2} + bc + ab + b^{2}

⇒ b^{2} = ac

We know if a,b,c are consecutive terms of GP then b^{2} = ac holds.

∴ a,b,c are in GP.

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