The sum of first 8 terms and first 24 terms of an A.P. are equal. Find the sum of its 32 terms.

The sum of first 5 terms and first 15 terms of an A.P. are equal. Find the sum of its first 20 terms.

The sum of first 5 terms and first 15 terms of an A.P. are equal. Find the sum of its first 20 terms.

The sum oif the first ten terms of an A.P. is equal to 155, and the sum of the first two terms of a G.P. is 9. Find these progressionsif the first term of the A.P. equals the common ratio of the G.P. and the 1st term of G.P. equals the common difference of A.P.

The sum of first p- terms terms of an A.P. is q and the sum of first q terms is p, find the sum of first (p + q)

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

The sum of the first 8 terms of an A.P. is 100 and the sum of its first 19 terms is 551. Find the first term and the common difference of the AP.

The sum of the first p terms of an A.P. is q and the sum of the first q terms of the same A.P. is p. Find the sum of the first (p+q) terms of the A.P.

If the sum of the first 9 terms of an AP is equal to the sum of its first 11 terms, then find the sum of its first 20 terms.

If the sum of the first 9 terms of an AP is equal to the sum of its first 11 terms, then find the sum of its first 20 terms.

If the sum of the first four terms of an AP is 40 and the sum of the first fourteen terms of an AP is 280. Find the sum of first n terms of the A.P.