Sum of Terms

In the sequence of numbers 2,5,3,\cdots, 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 100 terms of this sequence?
Source: NCTM Mathematics Teacher, December 2005

SOLUTION
The terms are 2,5,3,\textrm{-}2,\textrm{-}5,\textrm{-}3,2,5,3,\textrm{-}2,\textrm{-}5,\textrm{-}3,2,5,3,\textrm{-}2,\textrm{-}5,\textrm{-}3,\cdots
The sum of every six terms equal 0. If we divide the first 100 terms into six, we get
100=16(6)+4
All the first 96 terms sum to zero and the last four terms sum to
2+5+3+(\textrm{-}2)=8

Answer: 8

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About mvtrinh

Retired high school math teacher.
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