It's much more useful if you put in those G7's as others have suggested, so you get something more like this as the foundation to work from.

C - A7 - D7 - G7 - C

C - A7 - D7 - G7

C - C7 - F - F7

C - A7 - D7 - G7 - C

I say "foundation to work from" because the chords you actually play are going to be more complex that what is written here. For example, the tonic C at any given moment may have an a note added, making it a C6. Also, the A7, D7, and G7 chords at any given moment may be A, D, and G, or A6, D6, and G6. The D7 chord, if played as as a C7 slid up two frets, but with the first string left open as an e note, is really a D9. Most important of all, that F7 at the end of the third line is ripe for many possible substitutions, including F6, D9, and various diminished chords.