"the sum" or "a sum", which should be preferred when referring to an amount of money of a given value?

Considering the following three sentences:

    I worked for three weeks for which I received the/a princely sum of $100.  

    Her divorce settlement included the/a lump sum of $2 million.  

    She was paid the/a mind-boggling sum of ten million pounds for that film.

Should we prefer the "the sum" version or the "a sum" version?