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.