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

(a) The sum of 'n' terms of a progression is n(n + 1). Prove that it is an A..P. Also find its 10th term. (b) The sum of 'n' terms of a progression is (3n^(2) - 5n). Prove that it is an A.P. (c) If the sum of n terms of a series is (5n^(2) + 3n) then find its first five terms.

If the sum to n terms of a sequence be n^(2)+2n then prove tht the sequence is an A.P.

The sum of n terms of a series is 2n^2+3n . Is the series arithmetic ? If so, find it.

The sum of n terms of an A.P. is 3n^(2)+n then its pth term is (A)6P+2(B)6P-2(C)6P-1 (D) none of these

The ratio of the sums of m terms and n terms of an A.P. is m^(2) : n^(2). Prove that the ratio of their mth and nth term will be (2m - 1) : (2n-1).

If the ratio of sum of m terms of an AP to the sum of n terms of the same AP is (m^(2))/(n^(2)) .Then prove that the ratio of its mth and nth terms is 2m-1:2n-1.

The sum of n terms of an A.P. is n^(2) + 3n . Find its 20th term.