The terms `a_1,a_2,a_3` form an arithmetic sequence whose sum is 18.The terms sum of all possible common difference of the A.P is ______.

The sum of n terms of an A.P is n^2 .Find the common difference.

The sum of P terms of an AP is P^2 . Find the common difference.

The sum to n terms of an A.P. is n^(2) . Find the common difference.

If S_(n) =nP +1/2 n (n-1) Q, where S_(n) is the sum of first n terms of an A.P. then the common difference of the A.P. will be-

If an A.P., the sum of 1st n terms is 2n^2 + 3n , then the common difference will

The first term of an A.P. is 5, the last term is 45 and the sum is 400. Find the number of terms and the common difference.

The sum of first ten terms of an A.P. is 155 and the sum of first two terms of a G.P. is 9. The first term of the A.P. is equal to the common ratio of the G.P. and the first term of the G.P. is equal to the common difference of the A.P. Find the two progressions.

Suppose that all the terms of an arithmetic progression (A.P.) are natural numbers. If the ratio of the sum of the first seven terms to the sum of the first eleven terms is 6: 11 and the seventh term lies in between 130 and 140, then the common difference of this A.P. is

Suppose that all the terms of an arithmetic progression (A.P) are natural numbers. If the ratio of the sum of the first seven terms to the sum of the first eleven terms is 6 : 11 and the seventh terms lies in between 130 and 140, then the common difference of this A.P, is

The first and last terms of an A.P. are a and l respectively. If S be the sum of the terms then show that the common difference is (l^(2) - a^(2))/(2S - (l+a)) .