Let \(a_{1},a_{2},\ldots\) be positive real number in G.P. for each \(n\), let \(A_{n},G_{n},H_{n}\) be respectively, the arithmetic mean, geometric mean, harmonic mean of \(a_{1},a_{2}\ldots a_{n}\). Find an expression for the geometric mean of \(G_{1},G_{2},\ldots G_{n}\) in terms of \(A_{1},A_{2},\ldots A_{n},H_{1},H_{2},\ldots.H_{n}\) if \(a,H,H_{2},b\) are in H.P.