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))`.

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)).

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 , 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_1S_2, S_3, respectively. Prove that S_3=3(S_2-S_1)dot

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)).

The sum of terms of a G.P if a_(1)=3,a_(n)=96 and S_(n)=189 is

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

Let S_n denote the sum of the first n tem of an A.P. If S_(2n)=3S_n then prove that (S_(3n))/(S_n) =6.

Let S_n denote the sum of first n terms of an AP and 3S_n=S_(2n) What is S_(3n):S_n equal to? What is S_(3n):S_(2n) equal to?

If S_n denotes the sum of first n terms of an A.P., prove that S_(12)=3(S_8-S_4) .