Question

if the sum of first p term of an AP is eqaul to the sum of first q terms then show that the sum of the first (P+Q) terms is zero (P is not equal to Q)​

Answer 1

Step-by-step explanation:

sum of first p terms Sp=p/2(2a+(p-1)d)

sum of first q terms Sq=q/2(2a+(q-1)d)

but he given Sp=Sq

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

p(2a+(p-1)d=q(2a+(q-1)d).......eqn 1

sum of first p+q terms S(p+q)=(p+q)/2(2a+(p+q-1)d

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

by simplify we get

=p(2a+(p-1)d)-q(2a+(q-1)d)

=0...from eqn 1

so l.h.s= R.H.S

hence proved

hope you understand

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