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, b^{2} = 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
c^{2} = (36)(40)
c = √1440 = 37.95