**We have sum of p terms i. e.**

S_{p }= 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

**S**_{p+q}-S_{p} = -a (p+q)q/p-1