In an A.P of which a is the first , if the sum of the first  p terms is zero, then the sum of the next q  terms is

Given Sp=0, therefore, p2[2a+(p−1)d]=0⇒d=−2ap−1 Sum of next q terms is sum of an A.P whose first term will be Tp+1=a+pd∴S=q2[2(a+pd)+(q−1)d]=q2[2a+(p−1)d+(p+q)d]=q20−(p+q)2ap−1=−a(p+q)qp−1