Question

If a, b, c are in A.P and a, mb, c are in GP then show that a, m2b, c are in H.P

Answer 1

a, b, c, are in AP .

⇒ b = (a + c)/2

a, mb, c are in GP,

⇒ mb = √ac

⇒ m2b2 = ac

⇒ m2b. b. = ac

⇒ m2b ((a + c)/2) = ac (∵ b = (a + c)/2)

⇒ m2b = 2ac/(a + c)

⇒ a, m2b, c are in H.P.