What is the sum of the first $p+q $ terms of this A.P.? The sum of the first $p $ terms of an A.P. is $q $ and the sum of the first $q $ terms of the same A.P. is $p $. Find the sum of the first $p+q $ terms of the A.P.
Answer given: $$-(p+q) $$

$$q=\frac{p(a+(p-1)d)}{2}\tag{1}$$
$$p=\frac{q(a+(q-1)d)}{2}\tag{2}$$
$$S_{p+q}=\frac{(p+q)(a+(p+q-1)d)}{2}$$
Do $(2)-(1)$ to get $-2=a+(p+q-1)d$
Therefore,
$$S_{p+q}=-(p+q)$$
