已知数列{an}中,a1=2,a2=4,a(n+2)=a(n+1)-an,则a10等于?
问题描述:
已知数列{an}中,a1=2,a2=4,a(n+2)=a(n+1)-an,则a10等于?
答
a1=2,a2=4,a(n+2)=a(n+1)-an所以a(3)=a(2)-a(1)=2.a(4)=a(3)-a(2)=-2,a(5)=a(4)-a(3)=-4
a(6)=-2,a(7)=2,a(8)=4,a(9)=2,a(10)=-2
答
由a(n+2)=a(n+1)-an,和a(n+3)=a(n+2)-a(n+1)
得an+a(n+3)=0,
所以an+a(n+9)=0,即有a1+a10=0,
所以a10=-2