CBSE Class 10 Answered
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.}
Asked by vrushali | 28 Feb, 2013, 11:54: AM
Expert Answer
Sp=Sq
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.
Answered by | 28 Feb, 2013, 01:12: PM
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