Question

If A, G, H are arithmetic, geometric and harmonic means between a and b respectively, then A, G, H are

Options

• in G.P.

• in A.P.

• in H.P.

• Real numbers

Answer 1

in G.P.

Explanation:

Let two numbers a and b respectively,

A.M. = `A = (a + b)/2`, G.M. = `G = sqrt(ab)`,

H.M. = `H = (2ab)/(a + b)`

⇒ `A xx H = (a + b)/2 xx (2ab)/(a + b) = ab = G^2`

`G^2 = H xx A`

∴ `G/A = H/G ⇒ A, G, H` are in G.P.