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

If S_(n) denotes the sum of n terms of a G.P., prove that: (S_(10)-S_(20))^(2)=S_(10)(S_(30)-S_(20))

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

In a G.P. if S_1 , S_2 & S_3 denote respectively the sums of the first n terms , first 2 n terms and first 3 n terms , then prove that, S_(1)^(2)+S_(2)^(2)=S_(1)(S_2+S_3) .

If S_1 ,S_2 and S_3 denote the sum of first n_1,n_2 and n_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) equals :