In the sequence that begins , each term after the first two (which are given as and ) equals the term preceding it minus the term preceding that one. What is the sum of the first 100 terms of the sequence?
Solution
This calls for a spreadsheet. See the one pasted in below. We don't even need to carry it out to the hundredth term as there is a pattern that repeats every six terms. In particular every sixth total is zero so that the 96th total is zero. That makes the hundredth total equal to 5.
