If `S_n = 3n^2+2n`, Then prove that series is in A.P

The sum of n terms of a series is (3n^(2)+2n) . Prove that it is an A.P.

The sum of first n terms of a certain series is given as 2n^(2)-3n . Show that the series is an A.P.

If in an A.P, S_n=n^2p and S_m=m^2p , then prove that S_p is equal to p^3

If the sum of first n terms of an A.P. series is n^(2) +2n, then the term of the series having value 201 is-

S_(n) is the sum of n terms of an A.P. If S_(2n)= 3S_(n) then prove that (S_(3n))/(S_(n))= 6

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 for a sequence (t_n) , S_n = 2n^2 + 5 , find t_n and show that the sequence is an A.P.

If the sum of n tems of a series be 5n^(2)+3n find its nth term.Are the terms of this series in A.P.?

If the sum of n tems of a series be 5n^2+3n , find its nth term. Are the terms of this series in A.P.?

The sum of n terms of a series is n(n+1) . Prove that it is an A.P. also find its 10th term.