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This question is largely why Lavelle would prefer we use the equation E = -hR/n^2 and couple it with the equation ΔE=Efinal-Einitial. This way you never have to be concerned about whether or not to use the higher energy level. You only have to know which energy level it started at (initial) and which it ended at (final).
If the electron is going from n=4 to n=2, then it would be going from an excited state to a lower energy state, which would make sense that the resulting Energy from the Rydberg equation would be negative, as energy would be emitted in this scenario. In the equation, n1 is the initial and n2 is always the final, and the equation works itself out to whether the resulting energy is positive or negative.
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