When three quantities a, b and c are in G.P., then the geometric mean "b" is calculated as follows.

Since these quantities are in G.P., the ratio of b/a and the ratio of c/b should give us the same number. In other words these ratios should be equal. That is,

                            b/a = c/b          

On cross multiplying these we have b.b = a.c. That is, b² = ac.

 Example

Find the geometric mean between the two numbers 36 and 40.

If c is the number between these two numbers, then the geometric mean is given by

         c²      =       (36)(40)

         c        =        √1440   = 37.95