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I think when an e- goes from n=3 to n=1 the change in energy is negative because its releasing energy (going from a higher energy state to a lower one, and the change in energy is measured as En(final) - En(initial)). Going from n=1 to n=3 should be a positive change in energy since you have to absorb energy to move up the energy levels.
Whenever a electron goes from a higher energy state to a lower one the electron's energy has decreased and the energy is released as electromagnetic radiation, so we use the negative sign to describe the change in energy. This can be calculated through E=-hR/n^2 and delta E= Ef-Ei. Hope this helps!!
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