Inserting n Harmonic Means between two quantities

Let a and b be two given quantities. It is required to insert n harmonic means h₁, h₂, h₃,....h_n between the quantities a and b.

Let d = common difference of the A.P.

Hence h₁, h₂,....h_n are the n harmonic means.

If A, G and H respectively are arithmetic, geometric and harmonic means of two positive quantities a and b, then

G² = A.H and A ≥G≥H