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Question 12

A sequence $$\{a_n\}$$ is generated by the rule, $$a_n = a_{n-1} - a_{n-2}$$ for $$n \geq 3$$. Given $$a_1 = 2$$ and $$a_2 = 4$$, then sum of the first 2019 terms of the sequence is given by

Computing terms shows the sequence is periodic with period 6, and the sum of any full period is 0. Since $$2019 = 6 \times 336 + 3$$, the total sum equals the sum of the first 3 terms, $$2+4+2=8$$.

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