Question

The first term of AP is 'a' and thr sum of first p term is zero Show that the sum of next 'q' term is -aq(p+q)/p-1​

Answer 1

Step-by-step explanation:

Sp=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

Hope this helps you!!