If `S_1, S_2, S_3` be respectively the sums of `n ,2n ,3n` terms of a G.P., then prove that `S1 2+S2 2=S_1(S_2+S_3)` .

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) 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 and S_3 are respectively the sum of n, 2n and 3n terms of a G.P., then prove that S_1(S_3 - S_2) = (S_2 - S_1)^2 .

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

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_2+S_3)=(S_1)^2+(S_2)^2

If S_1,S_2a n dS_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 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 .

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) 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) .