Answer
${\bf 97.26}\;\rm nm$
Work Step by Step
We know that the prediction of the wavelengths in the hydrogen absorption spectrum is given by
$$\lambda_{m\rightarrow n}=\dfrac{\lambda_0}{\dfrac{1}{m^2}-\dfrac{1}{n^2}}$$
where $m=1,2,3,..$, and $n=m+1,m+2,m+3,...$
If we let $m=1$,
$$\lambda_{1\rightarrow n}=\dfrac{\lambda_0}{\dfrac{1}{1^2}-\dfrac{1}{n^2}}$$
where $\lambda_0=91.18$ nm
$$\lambda_{1\rightarrow n}=\dfrac{91.18}{1-\dfrac{1}{n^2}}$$
Remember that $\lambda_{1\rightarrow 2}$ is the first longest wavelength, $\lambda_{1\rightarrow 3}$ is the second longest wavelength, and hence $\lambda_{1\rightarrow 4}$ is the third longest wavelength (which we need to find).
$$\lambda_{1\rightarrow 4}=\dfrac{91.18}{1-\dfrac{1}{4^2}}=\color{red}{\bf 97.26}\;\rm nm$$
