(a_3=a_1^2), (a_2=9)

[ ar^2=a^2,\quad ar=9 ]

If (a\neq0): (r^2=a), and (ar=9\implies r\cdot r^2=9\implies r^3=9\implies r=\sqrt[3]{9})

[ a=r^2=9^{2/3},\quad a_6=ar^5=r^2\cdot r^5=r^7=9^{7/3} ]

From (ar=9) and (ar^2=a^2): (a=r^2), so (r^3=9).

[ a_6=a r^5 = 9\cdot r^4 = 9\cdot r\cdot r^3 = 9\cdot r\cdot9 = 81r = 81\cdot9^{1/3}=9^{4/3}\cdot9= wait ]

(a_6=ar^5=9\cdot r^4=9\cdot(r^3)\cdot r=9\cdot9\cdot r=81\cdot9^{1/3})

Answer: (81\cdot\sqrt[3]{9})