A series S is defined by its two first members a₁ , a₂ and a recursive formula a_n=a_n-1- a_n-2 .

Evaluate a₂₀₁₄ if a₁=2013 and a ₂=1492.

Following the terms leads to a cycle of length 6:

a1 = a1
a2 = a2
a3 = a2-a1
a4 = -a1
a5 = -a2
a6 = a1-a2
a7 = a1
a8 = a2

So a2014=a4=-a1 so the answer is -2013

Posted by Jer on 2013-08-29 13:57:50