Question

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.​

Answer 1

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