The formula for mean proportion is, b^2=ac.. so , a=5 and c=20
, b^2=100, b=10. therefore , 10 is the mean proportional between 5 and 20
1 5 1

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The geometric mean of two numbers is also called the mean proportion between two numbers.  It is so because:

A : Mean = Mean : B  or   A/Mean = Mean / B

Mean² = AB     

Mean = √ (AB)  = √5*20  = √100 = 10