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)`.

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 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 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)).

If the sum of n, 2n and infinite terms of G.P. are S_(1),S_(2) and S respectively, then prove that S_(1)(S_(1)-S)=S(S_(1)-S_(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 are the sums of first n natural numbers, their squares and cubes respectively, show that 9S_2^ 2=S_3(1+8S_1)dot

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,S_3 are the sum of first n natural numbers, their squares and their cubes, respectively, show that 9S_2^2=S_3(1+8S_1) .

Let S_n denote the sum of first n terms of an A.P. If S_(2n)=3S_n , then find the ratio S_(3n)//S_ndot