数列{an}满足Sn+Sn+1=5/3an+1,a1=4求an

数列{an}满足Sn+Sn+1=5/3an+1,a1=4求an
数列{an}满足Sn+Sn+1=5/3an+1,a1=4求an

数列{an}满足Sn+Sn+1=5/3an+1,a1=4求an
Sn+S(n+1)=(5/3)a(n+1)=(5/3)[S(n+1)-Sn]
4Sn=Sn+1
Sn+1/Sn=4
则,Sn成等比数列
S1=a1
Sn=4*4^(n-1)=4^n
an=Sn-Sn-1=4^n-4^n-1

Sn+S(n+1)=(5/3)a(n+1)=(5/3)[S(n+1)-Sn]
4Sn=Sn+1
Sn+1/Sn=4
得到Sn是等比数列
S1=a1
Sn=4*4^(n-1)=4^n
an=Sn-Sn-1=4^n-4^（n-1）