Question
If the sum of p terms of an AP is q and the sum of q term is p, then the sum of p + q terms will be:
Answer: Option D
:
D
let first term be aand common difference be d
sopthterm=a+(p−1)d
andsumoffirstpterms=p2(2a+(p−1)d)=q
hence(2a+(p−1)d)=2qp....(1)andqthterm=a+(q−1)d
andsumoffirstqterms=q2(2a+(q−1)d)=phence(2a+(q−1)d)=2pq....(2)subtract(1)from(2)(p−q)d=2(qp−pq)=2(q2−p2)qso,d=−2(p+q)pq....(3)(p+q)thterm=(a+(p+q−1)d)andsumofitsfirst(p+q)term=(p+q)2(2a+(p+q−1)d)=(p+q)2(2a+(p−1)d+qd)=(2qp+qd)(p+q)2...from(1)=(2qp−2−2qp)p+q2...from(3)=−(p+q)
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:
D
let first term be aand common difference be d
sopthterm=a+(p−1)d
andsumoffirstpterms=p2(2a+(p−1)d)=q
hence(2a+(p−1)d)=2qp....(1)andqthterm=a+(q−1)d
andsumoffirstqterms=q2(2a+(q−1)d)=phence(2a+(q−1)d)=2pq....(2)subtract(1)from(2)(p−q)d=2(qp−pq)=2(q2−p2)qso,d=−2(p+q)pq....(3)(p+q)thterm=(a+(p+q−1)d)andsumofitsfirst(p+q)term=(p+q)2(2a+(p+q−1)d)=(p+q)2(2a+(p−1)d+qd)=(2qp+qd)(p+q)2...from(1)=(2qp−2−2qp)p+q2...from(3)=−(p+q)
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