The wavelength of the first member of the Balmer series in hydrogen spectrum is x A^o.
Then the wave length (in A^o) of the first member of Lyman series in the same spectrum is:

For Hydrogen z=1, for 1 st  member of Balmer series n₁​ =2,n₂​ =3$$\begin{gathered} \frac{1}{\lambda }=R\left[\frac{1}{n_1^2}-\frac{1}{n_2^2}\right] \\ =R\left[\frac{1}{2_{ }^2}-\frac{1}{3_{ }^2}\right] \\ \frac{1}{{\lambda }_1}=\frac{5R}{36}---------------\left(1\right) \end{gathered}$$

For 1 st  member of Lyman series (in same spectrum)n₁ =1,n₂ =2

$$\begin{gathered} \frac{1}{\lambda }=R\left[\frac{1}{n_1^2}-\frac{1}{n_2^2}\right] \\ =R\left[\frac{1}{1_{ }^2}-\frac{1}{2_{ }^2}\right] \\ \frac{1}{{\lambda }_2}=\frac{3R}{4}---------------\left(2\right) \end{gathered}$$

$\frac{{\lambda }_2}{{\lambda }_1}=\frac{5}{27}$