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在数列{an}中,a1=1,a2=5,an+2=an+1-an(?

2007-10-02 13:54:03h***
在数列{an}中,a1=1,a2=5,an+2=an+1-an(n∈N*)则a2005为?在数列{an}中,a1=1,a2=5,an+2=an+1-an(n∈N*)则a2005为?:因为an+2=an+1-an =an-an-1-a?

最佳回答

  • 因为an+2=an+1-an =an-an-1-an =-an-1 所以an=-an-3=an-6 , 所以a2005=a1999=.......=a1=1
    2007-10-02 14:36:09
  • a(n+2)=a(n+1)-an a1=1 a2=5 a3=a2-a1=4 a4=a3-a2=4-5=-1 a5=a4-a3=-1-4=-5 a6=a5-a4=-5+1=4 a7=a6-a5=4+5=9 a8=a7-a6=9-4=5 a9=a8-a7=5-9=-4 a10=a9-a8=-4-5=-9 a11=-5 a12=4 a13=9 a14=5 ...........a11=a5 a12=a6 a13=a7 a14=a8 a(n+2)=a(n+1)-an =an-a(n-1)-an=-a(n-1) ∴an=-a(n-3)=a(n-6) a(2005)=a(332×6+13)=a13=a7=9
    2007-10-02 15:08:04
  • 很赞哦! (157)