If the sum of first p terms of an A.P. is equal to the sum of the first q terms, then find the sum of the first (p+ q) terms.

If the sum of first 10 terms of an A.P. is 4 times the sum of its first 5 terms, then find the ratio of first term and common difference.

If the 12th term of an A.P. is -13 and the sum of the first four terms is 24, what is the sum of the first 10 terms ?

If the sum of first n terms of an A.P. is cn^(2) then the sum of squares of these n terms is

If the first term of an A.P. is 2 and the sum of the first five terms is equal to one-fourth of the sum of the next five terms, find the sum of first 30 terms.

Find the sum of first n terms of an A.P. whose nth term is 3n+1.

If the first term of an A.P. is 2 and the sum of the first five terms is equal to one-fourth of the sum of the next five terms, find the 20th term.

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.

If the sum of first 7 terms of an AP is 49 and that of 17, terms is 289, find the sum of first n terms.

If the sum of m terms of an A.P. is equal to the sum of either the next n terms or the next p terms, then prove that (m+n)(1/m-1/p)=(m+p)(1/m-1/n)dot