# Problem of the Week Problem D Follow the Sequence

The first four terms of an arithmetic sequence are $$x$$, $$2x$$, $$y$$, and $$x-y-6$$, for some integers $$x$$ and $$y$$. What is the value of the $$50$$th term in this sequence?

Note: An arithmetic sequence is a sequence in which each term after the first is obtained from the previous term by adding a constant. For example, $$3$$, $$5$$, $$7$$, $$9$$ are the first four terms of an arithmetic sequence.