Let 'F' be the first term of the A.P. and 'L' be the last term of the A.P.

Given:

a  =  ( p / 2 )( F + L )

b  =  ( q / 2 )( F + L )

c  =  ( r / 2 )( F + L ) 

Therefore:

( a / p )( q - r )  +  ( b / q )( r - p )  +  ( c / r )( p - q )   =   ( 1 / 2 )( F + L )  [  {q - r} + {r - p} + {p - q}  ]

                                                                                       =   0