已知数列{an}的前n项和为Sn,且满足Sn=3/2(an-1)(n∈正整数)

已知数列{an}的前n项和为Sn,且满足Sn=3/2(an-1)(n∈正整数)
答案我知道,但是n=1有s1=a1=3/2(a1-1) ==> a1=3
n>1有an=Sn-Sn-1 = 3/2 (an - 1) - 3/2 (an-1 - 1) ==>an=3*an-1 公比3的等比数列
an = 3^n;
这个不应该证明当n=1时符合an=3*an-1吗?为什么不用证明?我记得老师讲看到这种都应该验证啊!