Question
Mon February 13, 2012 By:

In an AP, Sp=q, Sq=p and Sr denotes the sum of first r terms. Then find the value of Sp+q.

Expert Reply
Wed February 15, 2012
Sp = p/2{2A + (p-1)D} = q , Sq = q/2{2A + (q-1)D} = p
On Subtracting the second equation from 1st we get ,
D = -2(p+q)/pq ,
Also On adding the two equations we get , 2A + (p+q-2)D/2 = p/q + q/p
Now , Sp+q = (p+q)/2{2A + (p+q-1)D} = (p+q)/2 {2A + (p+q-1)D} =
(p+q)/2{p/q + q/p - (p+q-2)D/2 + (p+q-1)D}
= (p+q)/2{ p2 + q2 -(p+q)2 }/pq    [ By substituting the value of D ]
= -(p+q)
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