a1=3>0
假设当n=k(k∈N+)时,ak>0,则a(k+1)=ak^2>0
k为任意正整数,因此对于任意正整数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,为定值
log3(a1)=log3(3)=1
数列{log3(an)}是以1为首项,2为公比的等比数列
log3(an) =1×2^(n-1)=2^(n-1)
an=3^[2^(n-1)]
数列{an}的通项公式为an=3^[2^(n-1)]