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If S1, S2 and S3 be respectively the sum...

If `S_1, S_2` and `S_3` be respectively the sum of n, 2n and 3n terms of a G.P .Prove that `S_1(S_3-S_2)=(S_2-S_1)^2`.

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If S_(1), S_(2), S_(3) be respectively the sums of n, 2n and 3n terms of a G.P., prove that, S_(1)(S_(3) - S_(2)) = (S_(2) - S_(1))^(2) .

The sum of n ,2n ,3n terms of an A.P. are S_1S_2, S_3, respectively. Prove that S_3=3(S_2-S_1)dot

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If the sums of n, 2n and 3n terms of an A.P. be S_(1), S_(2), S_(3) respectively, then show that, S_(3) = 3(S_(2) - S_(1)) .

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