Problem: In the sequence of numbers each term after the first two is equal to the term preceding it minus the term preceding that. The sum of the first one hundred terms of the sequence is
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Solution:
The first eight terms of the sequence are . Since the seventh and eighth terms are the same as the first and second, the ninth term will be the same as the third, etc.; i.e., the sequence repeats every six terms. Hence the sum of the first 96 terms is zero, and the sum of the first one hundred terms is .