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