The sum of first n terms of a series is `an^(2) + bn + c`. Show that c = 0 and the series is in A.P.

The sum of first n terms of a series is n^(2) + an + b . Show that b = 0 and the series is in A.P.

If the sum of first n terms of a series is 2n^(2) + 3n , find the series.

The sum of first r terms of a series is ar^(2) + br , find the first and 12th terms of the series.

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-

The sum of p terms of a series is 3p^(2) + 5p . Prove that the terms of the series form an A.P.

The sum of first n terms of a series is 3^(n)(a+b) when a, b are constants. Then the terms of the series are in

The sum of first n terms of the series a + ar + ar^(2) +…+ ar^(n-1) +… oo is -

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 rth term of a series is (2r + 1)2^(r ) , find the sum of first n terms of the series.

The sums of first n terms of two A.P.'s are in the ratio (3n+5) : (5n - 9). Show that their 4th terms are equal.