If a, b, c are in G.P. and x, y are the arithmetic means of a, b and b, c respectively, then prove that and
If a, b, c are in A.P. and x,y,z are in G.P., show that
Since a, b, c are in A.P.∴ b - a = c - b 2b = c + aHere, x, y, z are in G.P.Let r be the common ratio∴ y = xr, z = xr2Now, [By using (i)] = 1 . 1 = 1∴
Insert 5 G.M.'s between
Find the sum of first n natural numbers OrEvaluate
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and 
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2b = c + a
[By using (i)]
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