We consider a one-dimensional ionic crystal consisting of an arbitrary number of alternating positive and negative ions. We calculate exactly the energy per ion and uncover some interesting patterns. It is found that the energy per ion remains constant each time the size of the system increases by one ion if addition of such an ion leads to a system with a nonzero total charge. On the other hand, the energy per ion always decreases if addition of such an ion leads to a charge neutral system with a zero total charge. Explicit analytical results are provided.