数列{an}前N项和Sn.3Sn =(an-1),(n)为下标.求证{an}为等比数列

数列{an}前N项和Sn
3Sn =(an-1),(1)
当n>=2,
有:
3Sn-1=[a(n-1)-1],(2)
(1)-(2),
3an=an-an-1
an/an-1=-1/2,(n>=2)
当n=1,
3S1=3a1=a1-1
2a1=-1
a1=-1/2
所以
{an}是以a1=-1/2,-1/2为公比的等比数列