We have sum of p terms i. e.
Sp = p/2 (2a+(n-1)d)=0
or d=-2a/(n-1)d
also
Sum of next q terms means (Sum of p+q terms) - ( sum of p terms)
or sum of p+q terms because sum of p terms is 0
=> p+q/2 ( 2a +(n-1)d)
=> p+q/2 (2a + (n-1)(-2a/(n-1)d)
or
=> -a (p+q)q/p-1
Therefore, sum of the next q terms is given by
Sp+q-Sp = -a (p+q)q/p-1