In the sequence of numbers , each term (starting with the third) is equal to the term preceding it minus the term preceding that one. What is the sum of the first terms of this sequence?

Source: NCTM Mathematics Teacher, December 2005

**SOLUTION**

The terms are

The sum of every six terms equal . If we divide the first terms into six, we get

All the first terms sum to zero and the last four terms sum to

**Answer**:

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