Is the chord progression of this short piece C-G7-C? I'm new to music theory and want to confirm my understanding.
The first two measures outline a C major chord. Since there are no other notes involved, C major is the interpretation.
The next two measures outline a G7 chord, even though the B is excluded. Since the previous two measures were G major, G7 is the principle option here.
The final measure is again C major for the same reason as the first two measures, reinforced by the fact that C major would be the expected destination of the G7 chord.
It is basically I - V7- I, C - G7 - C. As bourn out by the triad notes of C major (C E G) and G7 (G D F). It's rather unusual, though, to omit the 3rd of a chord - this tells whether it's major or minor. That missing B♮ would make the chord definitely G7, although it could have been B♭, making Gm7, often heralding an F chord. So it's a little ambiguous as it stands.
From a beginner point of view, though, C - G7 - C will suffice. Not sure whether inversions are relevant here, as the notes are not in chord form, only sort of arpeggiated. The V7 chord usually contains notes 4 and 7, which make the tritone that sounds like it needs resolving. Interestingly, those are the two notes left out of the scale , when making the 'safe' pentatonic.