Let excited state correspond to n and its transition takes place to m and then m to 1.

$\Rightarrow \frac{1}{108.5nm} =R2^2(\frac{1}{m^2}-\frac{1}{n^2})$ ...(1)

$ \frac{1}{30.4 nm} =R2^2(\frac{1}{1^2}-\frac{1}{m^2})$ .......(2)

$ \frac{1}{108.5nm}+\frac{1}{30.4 nm} = 4R (\frac{1}{1^2}-\frac{1}{n^2})$

On Solving $n^2 = 25 , \Rightarrow n = 5$