What note is played on the A string at the 3rd fret?

The note played on the A string at the 3rd fret is C. To understand why this is the correct answer, it's important to consider the structure of the guitar and how the fretboard is organized with musical notes.

The A string, when played open, is tuned to an A note. As you move up the fretboard, each fret represents a half step in pitch. Therefore, when you play the 1st fret on the A string, you get an A# or Bb; at the 2nd fret, you play a B; and at the 3rd fret, you elevate the pitch again, resulting in a C note.

This series of movements up the fretboard from the open string demonstrates how the notes progress chromatically, which means each fret corresponds to each successive note in the musical alphabet. Thus, the 3rd fret of the A string produces a C note.