If the sum of first n,2n,3n terms of an A.P. be `S_1`,`S_2` and `S_3` respectively then prove that `S_3=3(S_2-S_1)`

If the sum of first n,2n,3n terms of an A.P. be S_1 , S_2 and S_3 respectively then prove that S_1+S_3=2S_2

If S_1,S_2 and S_3 be the sums of first n term ,of 2 n terms and of 3n terms of a G.P. respectively,then prove that- S_1(S_3-S_2)=(S_2-S_1)^2 .

If S_1,S_2 and S_3 be the sums of first n term ,of 2 n terms and of 3n terms of a G.P. respectively,then prove that- S_1^2+S_2^2=S_1(S_2+S_3) .

If S_n denotes the sum of first n terms of an A.P. prove that S_12=3(S_8-S_4) .

The sum of first n terms of an A.P. is S_n .If S_n=n^2p and S_m=m^2p(mnen) .Show that S_p=p^3 .

If S_n denotes the sum of the first n terms of an AP and if S_2n=3S_n then S_3n:S_n is equal to

If the sum of n terms of an A.P is S_n=3n^2+5n then find the Common difference:

The sum of fIrst n terms of an A.P series is 26n-2n^2 . Find the fifth term.

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) .

Find the sum of first n terms of the series 1.3 + 2.5 + 3.7 + 4.9 +…..