The first three spectral lines of H -atom in the Balmer series are...

$\dfrac{1}{{\lambda}_{1}} = R{z}^{2}\left(\dfrac{1}{{2}^{2}} - \dfrac{1}{{3}^{2}}\right)$

$\dfrac{1}{{\lambda}_{1}} = R{z}^{2}\dfrac{5}{36}$ $. . . ( i )$

For ${3}^{rd}$ line

$\dfrac{1}{{\lambda}_{3}} = R{z}^{2}\left(\dfrac{1}{{2}^{2}} - \dfrac{1}{{5}^{2}}\right)$

$\dfrac{1}{{\lambda}_{3}} = R{z}^{2}\dfrac{21}{100}$ $. . . ( ii )$

$( ii ) + ( i )$

$\dfrac{{\lambda}_{1}}{{\lambda}_{3}} = \dfrac{21}{100} \times \dfrac{36}{5} = 1 . 512 = 15 . 12 \times {10}^{- 1}$

$x \approx 15$