If the sum of first n terms of a series is `(n +12)`, then what is its third term?

If the sum of the first n terms of the series

If S_(n) the sum of first n terms of an AP is given by 2n^(2)+n, then find its nth term.

If the sum of first n terms of an A.P. is 3n^(2)-2n , then its 19th term is

If the sum of the first n terms of an A.P. is 4n - n ^(2), what is the first term (that is S _(1) ) ? What is the sum of first two terms? What is the second term ? Similarly, find the 3 ^(rd), the 10^(th) and ten n ^(th) terms.

(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 of the first n terms of series be 5n^(2)+2n , then its second term is