(1)数列{an}中,a1=1,a2=-3,a(n+1)=an+a(n+2),则a2005=____(2)已知数列{an}满足a1=1,a1×a2×a3…an=n^2,求an.

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(1)数列{an}中,a1=1,a2=-3,a(n+1)=an+a(n+2),则a2005=____(2)已知数列{an}满足a1=1,a1×a2×a3…an=n^2,求an.

(1)数列{an}中,a1=1,a2=-3,a(n+1)=an+a(n+2),则a2005=____(2)已知数列{an}满足a1=1,a1×a2×a3…an=n^2,求an.
(1)数列{an}中,a1=1,a2=-3,a(n+1)=an+a(n+2),则a2005=____
(2)已知数列{an}满足a1=1,a1×a2×a3…an=n^2,求an.

(1)数列{an}中,a1=1,a2=-3,a(n+1)=an+a(n+2),则a2005=____(2)已知数列{an}满足a1=1,a1×a2×a3…an=n^2,求an.
an=a(n+1)-a(n+2)
a(n+1)=a(n+2)-a(n+3)
所以an=-a(n+3)=a(n+6)
所以6次一循环
2004被6整除 所以2005=1
a1×a2×a3…an=n^2
a1×a2×a3…an-1=(n-1)^2
an=(n/n-1)^2

1)
1,-3,-4,-1,3,4,1,-3,-4,-1,3,4
1,-3,-4,-1,3,4循环,
2005/6=334余 1
a2005=1
2)a1×a2×a3…an=n^2
a1×a2×a3…an-1=(n-1)^2
两者相除
an=(n/n-1)^2

1、成周期函数,a3=a2-a1=-4,a4=a3-a2=-1,
a5=a4-a3=3,a6=a5-a4=4,a7=a6-a5=1=a1
所以T=6,2005/7=333......3,a2005=a1=1
2、a1×a2×a3…an=n^2
a1×a2×a3…a(n-1)=(n-1)^2,两式相除
an=n^2/(n-1)^2