Answer
It should jump to the state $n = 1$
Work Step by Step
In the ground state state, $n = 1$
When the atom is in the third excited state, then $n = 4$
To emit light, the electron must jump down to a lower state where $n \lt 4$
Note that light with a shorter wavelength has more energy than light with a longer wavelength.
To emit light with the shortest possible wavelength, the electron must jump down to the state that maximizes the energy difference between states.
It should jump to the state $n = 1$
