设数列{an}的前n项和为Sn且an≠0(n∈N*),S1,S2...,Sn...成等比数列,

S1,S2...,Sn...的首项S1=a1,设公比为q,an≠0,所以q≠1.则Sn=a1q^(n-1),(n=1,2,...),S(n-1)=a1q^(n-2),(n=2,3,...),相减,an=Sn-S(n-1)=a1q^(n-1)-a1q^(n-2)=a1(q-1)q^(n-2),(n=2,3,...),这正说明a2,a3,a4...成等比数...