Question

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

Answer 1

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