Hello I was having trouble with this problem and was wondering if anybody could help me with it. Show that if the sum of the first p terms of an arithmetic progression is equal to the sum of the first q terms, where p $\displaystyle \not= $ q, then the sum of the first p + q terms must be zero.

I do not really know where to start; I came up with this but it is not helpful:

$\displaystyle \frac{p}{2}(2a + (p-1)d) = \frac{q}{2}(2a + (q-1)d) $

which of course shows that p = q even though it does not.

Thanks and happy new year!