# Sum of the

Given: Sp = a, Sq = b, and Sr = c

To Prove: Proof:

Let a1 be the first terms and d be the common difference of the A.P.

We know that sum of n terms of an A.P is given by: where, a = first term
n = nth terms
d = common difference

Therefore, we have,

Sum of first p terms =  ......(1)

Sum of first q terms =  ......(2)

Sum of first p terms =  .....(3)

Subtracting (2) from (1)   Subtracting (3) from (2)   From (IV) and (V), pq (p – q) (2br – 2cq) = qr (q – r) (2aq – 2bp)

p (p – q) (2br – 2cq) = r (q – r) (2aq – 2bp)

(aqr – bpr) (q – r) = (bpr – cpq) (p – q)

Dividing both sides by pqr   Hence, proved.

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