[fatberg]

I have been asked to determine n₁ and n₂ for a (given) series. I understand that series are defined by having a constant n₁ but is there a way to calculate it?

I have been given the Rydberg constant, the lowest energy line wavelength in nm, and the wavelength for the 6th line of the series. I've tried to form an algebraic equation but end up with reciprocal quadratics which are beyond the scope of what is required.

[Meter]

What is the problem saying? Sometimes the principal quantum number can be extracted from knowledge of the electron configuration.

Otherwise the equation I suspect you are trying to use is given here: https://en.wikipedia.org/wiki/Rydberg_formula#For_hydrogen

Correct?

[Borek]

You can always try brute force approach, calculate series for several different n/n pairs and see which fits.

In general it should be doable just by writing a series of simultaneous equations in two unknowns. Yes, solving can be difficult, as these equations are non-linear.