In an A.P., if the pth term is and the qth term is prove that the sum of the first pq terms must be where

Let a be the first term and d be the common difference.
                                           ...(i)
                                               ...(ii)
Subtracting (ii) from (i), we get
            or          
or                             or                            
Using this value in (i), we get
                            or              
or                             or