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Algebra Difficulty 3.0 AMC 10/12 Prove it United Kingdom

In the sequence $20, 18, 2, 20, -18, \ldots$ the first two terms $a_1$ and $a_2$ are 20 and 18 respectively. The third term is found by subtracting the second from the first, $a_3 = a_1 - a_2$ . The fourth is the sum of the two preceding elements, $a_4 = a_2 + a_3$ . Then $a_5 = a_3 - a_4$ , $a_6 = a_4 + a_5$ , and so on. What is the sum of the first 2018 terms of this sequence?

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