The sum of n terms of a series is `(2n^(2)+n)`.Show 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.

The sum of n terms of an A.P. series is (n^(2) + 2n) for all values of n. Find the first 3 terms of the series:

The sum of n terms of an A.P. is 4n^(2) + 5n. Find the series.

The ratio of the sum of m and n terms of an A.P. is m^(2) :n^(2) . Show that the ratio mth and nth term is (2m-1) : (2n-1).

The ratio of the sum of m and n terms of an A.P. is m^(2) :n^(2) . Show that the ratio mth and nth term is (2m-1) : (2n-1).

The ratio of the sums of m and n terms of an A.P. is m^2: n^2 .Show that the ratio of m^(t h) and n^(t h) term is (2m" "-" "1)" ":" "(2n" "-" "1) .

If the sum of n terms of an A.P. is 2n^2+3n then write its nth term.

If the sum of n terms of an A.P. is 2n^(2)+5n , then its n^(th) term

The nth term of a sequence is given by a_n=2n^2+n+1. Show that it is not an A.P.