Question

if the sum of first p terms of an AP is equal to the sum of first q terms then show that the sum of its first (p+q) terms is 0​

Answer 1

Answer:

Step-by-step explanation:

Sp=Sq

P/2(2a+(p-1)d)=q/2(2a+(q-1)d)

P(2a+pd-d)=q(2a+qd-d)

2ap p^2d-pd=2aq+q^2d-qd

2ap-2aq+p^2d-q^2d-pd+qd=0

2a(p-q)+d(p^2-q^2)-d(p-q)=0

2a(p-q)+d(p+q)(p-q)-d(p-q)=0

Take (p-q) common

(p-q)(2a+d(p+q)-d)=0

2a+d(p+q-1)=0/(p-q)

2a+(p+q-1)d=0

A(p+q)=0