Question

The first term of an ap is a and the sum of first p terms is 0 show that the sum of its next q terms is -a(p+q)q/p-1

Answer 1

let the first term and common difference of AP is a and d....

sum of first q terms =sum of first p terms =k

q/2{2a+(q-1)d} = p/2{2a+(p-1)d} = k

2a = 2k(q+p-1)/pq

and

d=-2k/pq

now sum of first p+q terms =Sp+q= p+q/2 {2a +(p+q-1)d}

=(p+q)/2{2k(p+q-1)/pq - 2k(p+q-1)/pq }

=0

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