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

Question

Philoid · Accepted Answer

Given are in AP.

⇒ {taking arithmetic mean – to get the relationship}

⇒

⇒ ab + ac + b² + bc = b² + bc + ab + b²

⇒ b² = ac

We know if a,b,c are consecutive terms of GP then b² = ac holds.

∴ a,b,c are in GP.