Shortest wavelength means maximum energy in transition.
Therefore for Balmer series transition would be n=∞ton=2 and for Brackett series transition would be from n=∞ton=4.
Now from Rydberg's formula,
λBr1λBl1=RH(421−∞21)RH(221−∞21)⇒λBr=4λBl=4λ