Thu February 28, 2013 By: Vrushali

If the sum of p terms of an AP is equal to the sum of q terms,then show that the sum of its p+q terms is zero.{plz. answer fast.}

Expert Reply
Thu February 28, 2013


p/2[2a +(p-1)d]=q/2 [2a+(q-1)d]

p[2a +pd - d]=q[2a+qd - d ]

2ap + p2d - pd =2aq + q2d -qd

2ap-2aq +p2d -q2d -pd +qd =0

2a (p-q) +(p+q)(p-q)d -d(p-q)=0

(p-q)[2a + (p+q)d - d ]=0

(p-q)/2[2a + (p+q)d - d ]=0

Hence, the sum of its first (p+q) terms is 0.

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