If the arithmetic progression whose common difference is nonzero the sum of first `3n` terms is equal to the sum of next `n` terms. Then, find the ratio of the sum of the `2n` terms to the sum of next `2n` terms.

In an A.P, the sum of first 2n terms is equal to the sum of next n terms. Then the ratio of the sum of first 3n terms to the next n terms is

Consider an arithmetic progression whose first term is a . if the sum of the first ten terms is zero and the sum of next ten terms is -200 then find the value of a .

The first term of an A.P. is 3.The sum of first 25 terms is equal to the sum of next 15 terms.Find the common difference of the A.P.

If in an A.P.the sum of m terms is equal to n and the sum of n terms is equal to m then prove that the sum of (m+n) terms is -(m+n)

If the sum of m terms of an A.P is equal to these that n terms and also to the sum of the next p terms,prove

If the sum of m terms of an A.P is equal to these that n terms and also to the sum of the next p terms,prove

If the first term of an AP is 2 and the sum of the first five terms is equal to one-fourth of the sum of the next five terms, then what is the sum of the first ten terms?

The sum of the first n-terms of the arithmetic progression is equal to half the sum of the next n terms of the same progression.Find the ratio of the sum of the first 3n terms of the progressionto the sum of its first n-terms.

The sum of first 2n terms of an AP is alpha .and the sum of next n terms is beta, its common difference is