Let a_{1},a_{2}, 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} a_{n}. Find an expression for the geometric mean of G_{1},G_{2}, G_{n} in terms of A_{1},A_{2}, A_{n},H_{1},H_{2},.H_{n} if a,H,H_{2},b are in H.P.: Sequence & Series (Mathematics)

Let

a_{1},a_{2},\ldots

be positive real number in G.P. for each\n

n

, let

A_{n},G_{n},H_{n}

be respectively, the arithmetic mean,\n geometric mean, harmonic mean of

a_{1},a_{2}\ldots a_{n}

. Find an\n expression for the geometric mean of

G_{1},G_{2},\ldots G_{n}

in\n terms of

A_{1},A_{2},\ldots A_{n},H_{1},H_{2},\ldots.H_{n}

if\n

a,H,H_{2},b

are in H.P.

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