Question

Qi. Iſ the sum of p terms ofan A.P is the same as the
sum of qterm show that the sum of its (p+q) term is 0. ​

Answer 1

Answer:

S

p

=S

q

⇒

2

p

(2a+(p−1)d)=

2

q

(2a+(q−1)d)

⇒ p(2a+(p−1)d)=q(2a+(q−1)d)

⇒ 2ap+p

2

d−pd=2aq+q

2

d−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

⇒ S

p+q

=0