In lesson 6, when Jon is explaining about the cadential progressions, he said that an authentic cadential progression must contain the root position dominant and tonic chord, which then later he explained that root position is not having inversions or seventh. But when he’s showing the PAC and IAC examples in C major, I see the V7 chord and I chord with inversions (ex in PAC with 1st soprano: G-B-D-F starting in the 2nd measure and E-G-C in the last two beats). Can anyone explain it to me? Thanks.
A root position chord can be a 7th or a triad.
I think where you may be confusing this is that a PAC must have a root position dominant chord, which can either be a triad or a 7th.
A half-cadence on the other hand, can only be a triad. Because the 7th causes too much pull back to tonic, you do not get the desired repose from a 7th in a half-cadence.
Remember though, this is a strict classical definition, as you get later into the romantic era, and early twentieth century, you find half-cadences with added 7ths. It is somewhat a matter of taste.
Thank you, sir