Question

In an ap of which is the first term if the sum of first P term is zero then sum of of next Q terms

Answer 1

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