The pth and qth terms of an A.P. are x and y respectively. Prove that the sum of (p + q) terms is.
`(p+q)/(2)[x+y+(x-y)/(p-q)].`

Explanation

To prove that the sum of the first (p + q) terms of an arithmetic progression (A.P.) is given by the formula:

\[ S_{p+q} = \frac{(p + q)}{2} \left[ x + y + \frac{(x - y)}{(p - q)} \right] \]

where the p-th term is \(x\) and the q-th term is \(y\), we can follow these steps:

...