If the sum of first p terms of an A.P. is equal to the sum of the first q terms, then
find the sum of the first (p+q) terms.
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Step-by-step explanation:
=Sq
⇒ 2p(2a+(p−1)d)=2q(2a+(q−1)d)
⇒ p(2a+(p−1)d)=q(2a+(q−1)d)
⇒ 2ap+p2d−pd=2aq+q2d−qd
⇒ 2a(p−q)+(p+q)(p−q)d−d(p−q)=0
⇒ (p−q)[2a+(p+q)d−d]=0
⇒ 2a+(p+q)d−d=0
⇒ 2a+((p+q)−1)d=0
⇒ Sp+q=0
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