数列{an}中,满足下列条件,求通项an ...数列{an}中,满足下列条件,求通项an①a(n+1)=1/3an+4②a1=2*n,(n+1),1为a的下标
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![数列{an}中,满足下列条件,求通项an ...数列{an}中,满足下列条件,求通项an①a(n+1)=1/3an+4②a1=2*n,(n+1),1为a的下标](/uploads/image/z/14263048-64-8.jpg?t=%E6%95%B0%E5%88%97%7Ban%7D%E4%B8%AD%2C%E6%BB%A1%E8%B6%B3%E4%B8%8B%E5%88%97%E6%9D%A1%E4%BB%B6%2C%E6%B1%82%E9%80%9A%E9%A1%B9an+...%E6%95%B0%E5%88%97%7Ban%7D%E4%B8%AD%2C%E6%BB%A1%E8%B6%B3%E4%B8%8B%E5%88%97%E6%9D%A1%E4%BB%B6%2C%E6%B1%82%E9%80%9A%E9%A1%B9an%E2%91%A0a%28n%2B1%29%3D1%2F3an%2B4%E2%91%A1a1%3D2%2An%2C%28n%2B1%29%2C1%E4%B8%BAa%E7%9A%84%E4%B8%8B%E6%A0%87)
数列{an}中,满足下列条件,求通项an ...数列{an}中,满足下列条件,求通项an①a(n+1)=1/3an+4②a1=2*n,(n+1),1为a的下标
数列{an}中,满足下列条件,求通项an ...
数列{an}中,满足下列条件,求通项an
①a(n+1)=1/3an+4
②a1=2
*n,(n+1),1为a的下标
数列{an}中,满足下列条件,求通项an ...数列{an}中,满足下列条件,求通项an①a(n+1)=1/3an+4②a1=2*n,(n+1),1为a的下标
∵a(n+1)=1/3an+4,a1=2,
∴an=1/3a(n-1)+4
=1/3²a(n-2)+4/3+4
.
=a1/3^(n-1)+4/3^(n-2)+4/3^(n-3)+.+4/3+4
=2/3^(n-1)+4(1/3^(n-2)+1/3^(n-3)+.+1/3+1)
=2/3^(n-1)+4[1-1/3^(n-1)]/(2/3)
=2/3^(n-1)+6[1-1/3^(n-1)]
=6-4/3^(n-1).
a(n+1)=1/3an+4
a(n)=1/3a(n-1)+4
=1/3[1/3a(n-2)+4]+4
=(1/3^2)a(n-2)+4(1+3)=(1/3^2)[1/3a(n-3)+4]+4(1+3)
=(1/3^3)a(n-3)+4(1+3+3^2)
=………………………………
=[1/3^(n-1)]a(1)+4[1+3+3^2+…+3^(n-2)]
=1/3^(n-1)+4{[3^(n-1))-1]/(3-1)]
=1/3^(n-1)+2*3^(n-1)-2