Q17 of 176 Page 20

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

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.

If a, b, c are in A.P. and a, b, d are in G.P., then prove that a, a – b, d – c are in G.P.

If pth, qth, rth and sth terms of an A.P., be in G.P., then prove that p – q, q – r, r – s are in G.P.

If x^a = x^b/2z^b/2 = z^c, then prove that are in A.P.

If a, b, c are in A.P. b, c, d are in G.P. and are in A.P., prove that a, c, e are in G.P.