If λ _ 1 and λ _ 2 are the wavelengths of the third member of Lyman...

$\dfrac{1}{{\lambda}_{1}} = R\left[\dfrac{1}{{1}^{2}} - \dfrac{1}{{4}^{2}}\right]$

$\dfrac{1}{{\lambda}_{2}} = R\left[\dfrac{1}{{3}^{2}} - \dfrac{1}{{4}^{2}}\right]$

$\dfrac{{\lambda}_{1}}{{\lambda}_{2}} = \dfrac{\left[\dfrac{1}{9} - \dfrac{1}{16}\right]}{\left[1 - \dfrac{1}{16}\right]} = \dfrac{7}{9 \times 15}$

$\dfrac{{\lambda}_{1}}{{\lambda}_{2}} = \dfrac{7}{135}$