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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

Let the sum of n, 2n, 3n terms of an A.P. be S_1, S_2 and S_3 , respectively, show that S_3 =3(S_2-S_1)

If Sn be the sum of n consecutive terms of an A.P. show that S_(n+4)-4S_(n+3)+6S_(n+2)-4S_(n+1)+S_n=0

If S_(n) be the sum of n consecutive terms of an A.P. show that, S_(n+3) - 3S_(n+2) + 3S_(n+1) - S_(n) = 0

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)) .

The sum of n term of three A.P are S_1,S_2, and S_3 . The frist term of each is 1 and common diffrence are 1,2,3 repectively .Prove that S_1+S_3 =2 S_2.

If S_(n) be the sum of n consecutive terms of an A.P. show that, S_(n+4) - 4S_(n+3) + 6S_(n+2) -4S_(n+1) +S_(n) = 0

If S be the sum, P the product and R the sum of the reciprocal of n terms in G.P., prove that, p^(2) = ((S)/(R ))^(n) .

If S_n be the sum of the n consecutive terms of an A.P,find the value of S_(n+3)-3S_(n+2)+3S_(n+1)-Sn

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