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`

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))

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 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 sums of n terms of three arithmetical progressions are S_(1),S_(2) and S_(3). The first term of each unity and the common differences are 1,2 and 3 respectively.Prove that S_(1)+S_(3)=2S_(2)

If S_(1) be the sum of (2n+1) term of an A.P. and S_(2) be the sum of its odd terms then prove that S_(1):S_(2)=(2n+1):(n+1)

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

If S_(1),S_(2),S_(3) be respectively the sums 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_(n) denotes the sum of first n terms of an A.P. If S_(2n) = 5(S_n) , then prove (S_(6n))/(S_(3n))=17/8

If S_(1),S_(2) andS _(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)