Junior Mathematical Olympiad 2005 Section B Q11

The first three terms of a sequence are $\frac{1}{4},\frac{1}{3},\frac{1}{2}$. The fourth term is $\frac{1}{2}-\frac{1}{3}+\frac{1}{4}$; henceforth, each new term is calculated by taking the previous term, subtracting the term before that, and then adding the term before that. Determine the 100th term of the sequence. (You may wish to write out the first few terms of the sequence first)