The sum of first n terms of an A.P. is m and that of first m terms is n. Prove that the sum of first m + n terms is `-(m + n)`.

The sum of first P terms of an A.P. is equal to that of the first Q terms. Prove that the sum of first (P+Q) terms is zero.

If the sum of first nine terms of an A.P is 171 and that of first 24 terms is 996,find the sum of first 41 terms.

The sum of first nine terms of an A.P. is 171 and that of 24 terms is 996. Find the sum of first 16 terms.

The first term of an A.P. is a. If sum of first p terms is zero, prove that the sum of first (p + q) terms is [a(p+q)q]/(1-p) .

The sum of fIrst n terms of an A.P series is 26n-2n^2 . Find the fifth term.

If the sum of the first n terms of an AP is 4n-n^2 ,what is the first term(that is S_1 )?What is the sum of first two terms?What is the second term?Similarly,find the 3rd,the 10th and nth terms.

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

The seventh term of an A.P. is 20 and the sum of first twenty terms is 610. Find the tenth term and the sum of first fifteen terms.

In an A.P. the nth term is p and the sum of first n terms is q. Show that the first term of the series is (2q-pn)/n .

The sum of first ten terms of an A.P. is 120. The sum of next ten terms is 320. Find the first term and common difference.