a1=3>0
假設當n=k(k∈N+)時,ak>0,則a(k+1)=ak^2>0
k為任意正整數(shù),因此對于任意正整數(shù)n,an恒>0
a(n+1)=an^2
log3[a(n+1)]=log3(an^2)=2log3(an)
log3[a(n+1)] /log3(an)=2,為定值
log3(a1)=log3(3)=1
數(shù)列{log3(an)}是以1為首項,2為公比的等比數(shù)列
log3(an) =1×2^(n-1)=2^(n-1)
an=3^[2^(n-1)]
數(shù)列{an}的通項公式為an=3^[2^(n-1)]