Question
Tue July 26, 2011 By:
 

If the sum of p terms of an A.P. is equal to the sum of q terms then show that the sum of its p+q terms is zero.

Expert Reply
Tue July 26, 2011
Sp=Sq
=>p/2{2a+(p-1)d}=q/2{2a+(q-1)d}
=>2a(p-q)+{p(p-1)-q(q-1)}d=0
=>2a(p-q)+{(p2 -q2 )-(p-q)}d=0
=>(p-q){2a+(p+q-1)d}=0
=>2a+(p+q-1)d=0         [since p is not equal to q]
Now,Sm+n=(m+n)/2{2a+(m+n-1)d}
=> Sm+n=(m+n)/2*0=0
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