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

问题描述:

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.