在数列{an}中,a1=1,a2=2,a(n+2)=2/3a(n+1)+1/3an,求an+2)=2/3a(n+1)+1/3an,求an

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在数列{an}中,a1=1,a2=2,a(n+2)=2/3a(n+1)+1/3an,求an+2)=2/3a(n+1)+1/3an,求an
在数列{an}中,a1=1,a2=2,a(n+2)=2/3a(n+1)+1/3an,求an+2)=2/3a(n+1)+1/3an,求an

在数列{an}中,a1=1,a2=2,a(n+2)=2/3a(n+1)+1/3an,求an+2)=2/3a(n+1)+1/3an,求an
a(n+2)=2/3a(n+1)+1/3an
.
a3=2/3a2+1/3a1
全部相加左边=a3+..a(n+2)
右边=2/3a(n+1)+an+.+a3+a2+1/3a1
相消后
a(n+2)+1/3a(n+1)=7/3
(a(n+2)-7/4)=-1/3(a(n+1)-7/4)
a3=5/3 a3-7/4=-1/12
an-1是第三项是-1/12,公比-1/3的等比数列
an=((-3/4)(-1/3)^n)+1