How to express the ellipsis in predicate logic?

Question

Consider a statement like: the graph G has an infinite path. I'm trying to translate that into predicate logic. I keep finding myself relying on the crutch of the ellipsis, e.g. expressing a path as $a_1, a_2 ... a_k$, but the ellipsis is not allowed in predicate logic. So how can the statement be expressed? More generally, the ellipsis is used a lot in informal mathematical writing, so what is the standard strategy for eliminating it in predicate logic?