数列an中,an+2=an+1-an,a1=2,a2=5,则a2009

a(n+2)=a(n+1)-ana1=2,a2=5,∴a3=a2-a1=5-2=3a4=a3-a2=3-5=-2a5=a4-a3=-2-3=-5a6=a5-a4=-5-(-2)=-3a7=a6-a5=-3-(-5)=2a8=a7-a6=2-(-3)=5所以an是关于2,5,3,-2,-5,-3循环2009/6=334.5所以a2009=-5