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 Steven Zheng posted 2 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 Steven Zheng posted 2 months ago


Scroll to Top