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.

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) .

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

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 7 times the 7th term of an A.P is equal to 11 times its 11th term,Show that the 18th term of an A.P is zero.

The sum of the pth and the qth term of an A.P. is equal to the sum of rth and sth term of it. Show that (p-r)th term and (s-q)th terms are equal

Find the rth term of an A.P., the sum of whose first n terms is 2n+3n^2 .

The pth term of an A.P. is twice the qth term. Again the sum of qth and rth term is 2. Prove that the pth term is frac(4(q-p))(3q-2p-r)