In this paper, we consider arithmetic progressions contained in Lucas sequences of the first and second kind. We prove that for almost all Lucas sequences, there are only finitely many arithmetic three term progressions and their number can be effectively bounded. We also show that there are only a few Lucas sequences which contain infinitely many arithmetic three term progressions and one can explicitly list both the sequences and the progressions in them. A more precise statement is given for sequences with dominant zero.
展开▼