If `S_1`,`S_2`,........,`S_p` are the sums of `n` terms of an A.P

If S_1 , S_2 ,....... S_p are the sum of n terms of an A.P.,whose first terms are 1,2,3,...... and common differences are 1,3,5,7.....Show that S_1 + S_2 +.......+ S_p = [np]/2[np+1]

If s_(1), s_(2), s_(3)…..s_(p) are the sums of n terms of 'p' A.P's whose first terms are 1,2,3…p and common differences are 1,3,5… (2p-1) respectively then s_(1) + s_(2) + s_(3) + …+ s_(p) =

If S_(1), S_(2), S_(3) be the sums of n terms of three aA.P.'s, the first term of each A.P. being 1 and the respective common differences are 1, 2, 3 then show that, S_(1) + S_(3) = 2S_(2) .

If S_(1), S_(2), S_(3) are the sums of n, 2n, 3n terms respectively of an A.P., then S_(3)//(S_(2) - S_(1))-

If S_(n) danotes the sum of n terms of n terms of an A.P. then S_(n + 3) - 3 S_(n + 2) + 3S_(n + 1) - S_(n) =

If S_n , be the sum of n terms of an A.P ; the value of S_n-2S_(n-1)+ S_(n-2) , is

If S_(n), be the sum of n terms of an A.P; the value of S_(n)-2S_(n-1)+S_(n-2), is

Let S_(1) be the sum of the first n terms of the A.P 8,12,16,... and let S_(2) be the sum of the first n terms of the A.P 17,19,21,... assume n!=0 then S_(1)=S_(2) for