(1) A quantity corresponding to one of possibly several different definitions of the "average" of a set of values. Examples include the arithmetic mean and the geometric mean.
(2) The arithmetic mean (a.k.a. average).
If you want the arithmetic mean than the sum of the values will be the product of the arithmetic mean and the number of values.
I don't believe you can calculate the sum of the values with only the the number of values and the geometric mean or any of the other variations of the mean.