If `S_(1), S_(2), S_(3)` be the sum of n, 2n and 3n terms respectively of an A.P., prove that `S_(3)=3(S_(2)-S_(1))`.

If S_(1), S_(2), S_(3) are the sums of n, 2n, 3n terms respectively of an A.P., then S_(3)//(S_(2) - S_(1))-

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)

If S_(1),S_(2) andS _(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)

If S_1, S_2, S_3 are the sums to n, 2n, 3n terms respectively for a GP then prove that S_1,S_2-S_1,S_3-S_2 are in GP.

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

If S_(1),S_(2)andS_(3) denote the sum of first n_(1)n_(2)andn_(3) terms respectively of an A.P., then (S_(1))/(n_(1))(n_(2)-n_(3))+(S_(2))/(n_(2))+(n_(3)-n_(1))+(S_(3))/(n_(3))(n_(1)-n_(2)) =

If S_(1),S_(2),S_(3) be respectively the sum of n,2n and 3n terms of a GP, then (S_(1)(S_(3)-S_(2)))/((S_(2)-S_(1))^(2)) is equal to

If the sum of n,2n,3n terms of an AP are S_(1),S_(2),S_(3) respectively.Prove that S_(3)=3(S_(2)-S_(1))

If S_(n) denotes the sum of first n terms of an AP, then prove that S_(12)=3(S_(8)-S_(4)).