#math trivia for #April19:#110 is 10*11, 2 more than 9*12, 6 more than 8*13, 12 more than 7*14, etc.What’s the pattern?
— Burt Kaliski Jr. (@modulomathy) April 19, 2012
Let n be the index of the term, starting at 0. The terms follow the pattern:
110 = (10-n)*(11+n) + n*(n+1)
In other words, for each n, we can say:
110 is n*(n+1) more than (10-n)*(11+n) .
The formula can be checked by expanding it:
(10-n)*(11+n) + n*(n+1) = 110+n-n^2 + n^2+n = 110
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