设数列{an}满足a1=3,an>0,且 ,3an²=a（n-1）的五次方则通项an=?

3(an)^2 = [a(n-1)]^5
ln3 + 2ln(an) = 5ln(a(n-1))
2(ln(an)-(1/3)ln3 ) = 5( ln(a(n-1)) -(1/3)ln3 )
(ln(an)-(1/3)ln3 )/( ln(a(n-1)) -(1/3)ln3 ) = 5/2
(ln(an)-(1/3)ln3 )/( ln(a(1)) -(1/3)ln3 ) = (5/2)^(n-1)
ln(an)-(1/3)ln3 = ((2/3)ln3).(5/2)^(n-1)
ln(an) = ((2/3)ln3).(5/2)^(n-1) + (1/3)ln3
an = e^{((2/3)ln3).(5/2)^(n-1) + (1/3)ln3 }