Which series of the hydrogen spectrum was observed first?

Hydrogen atoms are excited from ground state to the state of principal quantum number $4$. Then,the number of spectral lines observed will be . . . . . . .

Let $F_1$ be the frequency of the second line of the Lyman series and $F_2$ be the frequency of the first line of the Balmer series. Then,the frequency of the first line of the Lyman series is given by:

What is the wavelength of the least energetic photon emitted in the Lyman series of the hydrogen atom spectrum? (in $nm$)

If the wavelengths of the first Lyman line for Hydrogen,$He^+$,and $Li^{2+}$ ions are $\lambda_1$,$\lambda_2$,and $\lambda_3$ respectively,then the ratio of these wavelengths is:

In the hydrogen spectrum,the shortest wavelength in the Balmer series is $\lambda$. The shortest wavelength in the Brackett series is $........\,\lambda$.