VectorMethod Sequence

2016

Problem - 3075

Starting at the origin, a bug crawls 1 unit up, 2 units right, 3 units down and 4 units left. From this new point, the bug repeats this entire sequence of four moves 2015 more times, for a total of 2016 times. The coordinates of the bugâ€™s final location are $(a, b)$. What is the value of $a + b$?