数列an中,an+2=an+1-an,a1=2,a2=5,则a2009

数列an中,an+2=an+1-an,a1=2,a2=5,则a2009
数列an中,an+2=an+1-an,a1=2,a2=5,则a2009

数列an中,an+2=an+1-an,a1=2,a2=5,则a2009
a(n+2)=a(n+1)-an
a1=2,a2=5,
∴a3=a2-a1=5-2=3
a4=a3-a2=3-5=-2
a5=a4-a3=-2-3=-5
a6=a5-a4=-5-(-2)=-3
a7=a6-a5=-3-(-5)=2
a8=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