See that the algorithm shown by Spartan does not match with the sequence given by mvdwege, so I cannot tell which of them is the correct one in T5.
The proper sequence (specifically for Soldier career after errata 0.6) is:
Promotion Officer --> Commission --> Promotion Enlisted
The actual sequence whether you've applied errata or not doesn't affect the point I was making that you don't get multiple promotions in a term.
In previous versions, if you went to Accademy (or OTC/NOTC in College) you began the second term as O1, while if you were promoted from the ranks (via comisión/OCS) you could begin it as O2. That made posible to have a quicker career in you promoted from ranks tan in you attand Accademy/College (unless you attand medical school, in which case you ended second term as O3).
Yes it makes it possible to have a quicker career, but does it make better officers? You spend four years as a private, you score well on a test, go to officer school and you become an 1st Lieutenant (O2). You've been a private all your career but now you can go straight into the role of commanding a platoon? Thats without any time learning how to command a section and learning all the practicalities of being an officer. It would be okay to start at O2 if you'd risen to be an NCO of Sergeant rank and done a very similar job to a junior officer. Thats the real world view.
The in game explanation is that T5 assigns skills differently during the course of your career, so you don't have to worry about gaining high rank before you muster out unless you want some of the automatic skills that go with rank or you want the maximum from your muster out benefits.