Which series of the hydrogen spectrum was observed first?

In the hydrogen spectrum,the shortest wavelengths of the Lyman and Balmer series are $\lambda_1$ and $\lambda_2$ respectively. The Rydberg constant of hydrogen is

The wavelength of the first line of the Balmer series of a hydrogen atom is $\lambda \ \mathring{A}$. The wavelength of the same line for a doubly ionized lithium atom $(Z = 3)$ is:

The ratio of wavelengths of the last line of the Balmer series and the last line of the Lyman series is

If ${\lambda _{{\text{max}}}}$ is $6563 \text{ Å}$, then the wavelength of the second line of the Balmer series will be:

The lines in the Balmer series have their wavelengths lying between