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_1(S_2-S_1)^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_2+S_3)=(S_1)^2+(S_2)^2

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

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)

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

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

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 :

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) .