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_(n)=n^(2)a+(n)/(4)(n-1)d is the sum of the first n terms of an arithmetic progression, then the common difference is

If S_(1),S_(2)andS_(3) denote the sum of first n_(1)n_(2)andn_(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)) =

If S_(1), S_(2) and S_(3) are the sums of first n natureal numbers, their squares and their cubes respectively, then (S_(1)^(4)S_(2)^(2)-S_(2)^(2)S_(3)^(2))/(S_(1)^(2) +S_(2)^(2))=

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 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 :

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 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) .

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

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 AP are S_1,S_2,S_3 respectively . Prove that S_3=3(S_2-S_1)