且a1=a-1=0,
an=Sn-Sn-1=(an-1)-(an-1-1)=0,(n>1)
an-1=Sn-1-Sn-2=(an-1-1)-(an-2-1)=0,
∴an-an-1=0,
∴数列{an}是等差数列.
②当a≠1时,
a1=a-1,
an=Sn-Sn-1=(an-1)-(an-1-1)=an-an-1,(n>1)
an-1=Sn-1-Sn-2=(an-1-1)-(an-2-1)=an-1-an-2,(n>2)
an |
an−1 |
an−an−1 |
an−1−an−2 |
∴数列{an}是等比数列.
综上所述,数列{an}或是等差数列或是等比数列.
故选C.