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)` .

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))

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_(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_(n) denotes the sum fo n terms of a G.P. whose first term and common ratio are a and r respectively then show that: S_(1)+S_(3)+S_(5)+……..+S_(2n)-1=(an)/(1-r)-(ar(1-r^(2n)))/((1-r^(2))

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_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)and s_(3) are the sum of first n , 2n, 3n terms respectively of an arithmetical progression , then show that s_(3)=3 (s_(2)-s_(1))

If S_1,S_2,S_3,………….S_n denote the sum of 1,2,3…………n terms of an A.P. having first term a and S_(kx)/S_x is independent of x then S_1+S_2+S_3+……..+S_n= (A) (n(n+1)(2n+1)a)/6 (B) ^(n+2)C_3a (C) ^(n+1)C_3a (D) none of these