In hydrogen spectrum the shortest wave length of Lyman & Balmer series are  ${\lambda }_1\&{\lambda }_2$   respectively the rydberg constant of hydrogen is

In hydrogen spectrum 
Short wave length of lyman series $n_1=1,n_2=\infty$  
$\frac{1}{{\lambda }_1}=R\left(\frac{1}{12}\right)=\frac{R}{1}$
In balmer series $n_1=2,n_2=\infty$  
$\frac{1}{{\lambda }_2}=R\left(\frac{1}{2^2}\right)=\frac{R}{4}=R\left[\frac{3}{4}\right]$
$R=\frac{4}{3}\left[\frac{{\lambda }_2-{\lambda }_1}{{\lambda }_1{\lambda }_2}\right]$
$R=\frac{4({\lambda }_2-{\lambda }_1)}{3{\lambda }_1{\lambda }_2}$