Question

If the pth term of an arithmetic progression is \( \frac{1}{q} \) and the qth term is \( \frac{1}{p} \) , prove that the sum of the first pq terms must be \( \frac{1}{2}(pq+1) \).

Answer 1

Solution:

Let a be the first term and d the common difference.

Proceed as follows:

Hence, the sum of the first pq terms is \( \frac{1}{2}(pq+1) \).

The sum is \( \frac{1}{2}(pq+1) \) is proved.