Question
Wed August 29, 2012 By: Vaishnavi

prove that:

Expert Reply
Wed August 29, 2012
Let A and D be the first term and common difference of A.P.
 
From the given information, we have:
A + (p– 1) D = a … (1)
 A + (q – 1) D = b … (2)
A + (r – 1) D = c … (3)
 
a (q – r) + b (r – p) + c (p – q)
= [A + (p– 1) D] (q – r) + [A + (q – 1) D] (r – p) + [A + (r – 1) D] (p – q)]
= A (q – r) + (p – 1) (q – r)D + A (r – p) + (q – 1) (r – p) D + A (p – q) + (r – 1) (p – q) D
= A (q – r + r – p + p – q) + D (pq – pr – q + r + qr – pq – r + p + pr – rq – p + q)
= A (0) + D (0)
= 0
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