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, b^2=100, b=10. therefore , 10 is the mean proportional between 5 and 20

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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

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

Mean² = AB

Mean = √ (AB) = √5*20 = √100 = 10