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 sums 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 9 S_(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 the ratio ( S_(3n))/( S_(n)) is equal to :

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?

Let S_(n) denote the sum of the first n terms of an A.P. If S_(2n) = 3S_(n) , then S_(3n) : S_(n) is equal to :

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.L , 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)) is equal to :

IF a A.P. if T_n=4n+3 . Find S_13 .

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 the sum of n terms of an A.P. is given by : S_(n) = 3n+ 2n^(2) , then the common difference of the A.P. IS :

If the sum of n terms of an A.P. is given by S_(n)=n^(2)+n , then the common difference of the A.P. is