The idea is simple. The ordinary average, or arithmetic mean, of, say, 5 numbers is

 

(a + b + c + d + e) / 5,

 

and the geometric mean is

 

Again, the preparation for the lecture is noting that this word appears in the book, listing it in your list of concepts, and then researching the meaning of the word.

 

Mathematics works with generalizations. The geometric mean is a logical generalization of the arithmetic mean. This point should be stressed.

 

A useful educational tool is to explain what a concept is not. After explaining the concept of the geometric mean, say it is not the arithmetic mean.