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2018 AMC 12B Question 18

AMC12 · 2018 AMC 12B

Question 18

A function $f$ is defined recursively by $f(1)=f(2)=1$ and $$
f(n)=f(n-1)-f(n-2)+n
$$ for all integers $n\ge3.$ What is $f(2018)?$
  1. $2016$
  2. $2017$
  3. $2018$
  4. $2019$
  5. $2020$