Question

如果数列{an}的前n项和sn满足对任意n∈N+,都有sn=3/2an-3,求证{an}为等比数列

Answer 1

S1=1.5a1-3=a1推出a1=6 又 Sn-Sn-1=an=1.5an-（1.5an-1）推出3an-1=an，故{an}为等比数列

Answer 2

当n>2时，
Sn-Sn-1 =3/2(an-an-1) =an
所以 0.5an=1.5an-1
所以 an=3an-1
当n=1时，s1=a1=6

所以 {an}为等比数列