已知数列{an}满足a1=1,a2=2,a(n+2)=a(n+1)-an,则a100=____________

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已知数列{an}满足a1=1,a2=2,a(n+2)=a(n+1)-an,则a100=____________
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已知数列{an}满足a1=1,a2=2,a(n+2)=a(n+1)-an,则a100=____________
已知数列{an}满足a1=1,a2=2,a(n+2)=a(n+1)-an,则a100=____________

已知数列{an}满足a1=1,a2=2,a(n+2)=a(n+1)-an,则a100=____________
a(n+2)=a(n+1)-an
a(n+1)=an -a(n-1)
所以
a(n+2) = -a(n-1)
an = -a(n-3) = a(n-6)
a(100) = a(100 - 16*6) = a4 = -a1 = -1
别只出题,不处理题哟.该采纳一些了.

4

这个数列应该为
1,2,1,-1,2,3,1,-2,-3,-1,2,3,1,-2,-3,
,-1,2,3,1,-2,-3,六个数循环
(100-3)/6=16余1
答案为-1

6个一周期
答案为-1

a(100=)a(98+2)=a(98+1)-a(98)=a(99)-a(98)-----1式,以此类推。a(99)=a(98)-a(97)------2式,a(99)=a(97)-a(96),1式减2式,以此类推,a(100)=a(2)-a(1)=2-1=1

1,2,1,-1,-2,-1,1,2,1,-1,-2,-1....
可见数列以每6个数为一个周期
100是除以6的余数为4,故,a100的值为6个数一个周期的第四个数
即a100=-1

-1