#### Fill Question

Given a sequence satisfying the condition

a_{n+2}+a_n=a_{n+1} and a_1=2 and a_2=3, then a_{2007}=

Collected in the board: Periodic function

Steven Zheng posted 5 months ago

#### Answer

1. a_{n+2}=a_{n+1}-a_n

a_{n+3}=a_{n+2}-a_{n+1}

Addition of two expressions , we get

a_{n+3}=-a_n

Therefore

a_{n+6}=a_n

So the terms of this sequence has a period of 6 and repeat themselves every 6 terms.

a_{2017} = a_{336\times 6+1} =a_1 = 2

Steven Zheng posted 5 months ago

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