Yes, I was about to say something like this myself, that is,
    that "a final arrow" implies the shooter still has some more
    in the quiver, whereas "the final arrow" implies the quiver
    is now empty.
 
    BUT...that ceases to be the case if we add a phrase: "He shot
    the final arrow of the day."  Which leads to another
    question: Could we substitute "a" for "the" in that sentence
    and have a "grammatically correct" sentence?   My own feeling
    is that I would consider "He shot a final arrow of the day."
    as being "uncolloquial"--really meaninging that it is
    "ungrammatical."
 
    Norm Carlson