Prove that the sum of an odd number of terms in A.P is equal to the middle term mutiplied by the number of terms

If the sum of m terms of an A.P, is equal to the sum of n terms of the A.P ., then the sum of (m + n) terms is

In a sequence of 21 terms, the first 11 terms are in A.P. with common difference 2 and the last 11 terms are in G.P. with common ratio 2. If the middle term of the A.P. is equal to the middle term of the G.P., then the middle term of the entire sequence is

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 sum of p terms of an A.P is equal to the sum of q terms, then show that the sum of its p+q terms is zero.

If the sum of p terms of an A.P is equal to sum of q terms (p != q) then the sum of (p + q) terms is

The sum of three numbers in G.P. is 70. If the first and last term are multiplied by 4 and the middle term by 5, then they will be in A.P., find them.

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

An A.P., and a H.P. have the same first and last terms and the same odd number of terms. The middle terms of the three series are in

An A.P., and a H.P. have the same first and last terms and the same odd number of terms. The middle terms of the three series are in