已知数列{an}满足a1=1,a2=2,a(n+2)=2/3a(n+1)+1/3an,求an

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已知数列{an}满足a1=1,a2=2,a(n+2)=2/3a(n+1)+1/3an,求an
已知数列{an}满足a1=1,a2=2,a(n+2)=2/3a(n+1)+1/3an,求an

已知数列{an}满足a1=1,a2=2,a(n+2)=2/3a(n+1)+1/3an,求an
an=7/4 + 9/4 * (-1/3)^n
a(n+2)+a(n+1)/3=a(n+1)+an/3=a2+a1/3=7/3,
a(n+2)-a(n+1)=(-1/3)[a(n+1)-an]=[-1/3]^n*(a2-a1),
上下两个式子结合就可以得到an=7/4+9/4* (-1/3)^n