已知数列满足a1=1 ,an+1+2an=2 求an

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已知数列满足a1=1 ,an+1+2an=2 求an
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已知数列满足a1=1 ,an+1+2an=2 求an
已知数列满足a1=1 ,an+1+2an=2 求an

已知数列满足a1=1 ,an+1+2an=2 求an
a(n+1)+2an=1
a(n+1)-1/3=-2an+2/3=-2(an-1/3)
所以,{an-1/3}是以a1-1/3=2/3为首项,公比是-2的等比数列.
即an-1/3=2/3*(-2)^(n-1)
an=2/3(-2)^(n-1)+1/3

a=1, n+1+2n=2 , 3n=1 , n=1/3

由an+1+2an=2得3an=1
an=1/3