Geometric mean of 2 and 8 = sqrt(2*8) = sqrt(16) = 4
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The difference between arithmetic and geometric mean you can find in the following link: "Calculation of the geometric mean of two numbers".
You can find the differences between arithmetic and geometric mean in the following link: "Calculation of the geometric mean of two numbers".
Geometric mean between 2 and 24 is 6.928203230275509. Look at link: "Calculation of the geometric mean of two numbers".
Look 2 and 8, their geometric mean is square root of 16 which is 4 and between 2 and 54. 9 and 4 have a geometric mean of 6 which is also between 2 and 54. Is this what you mean? Pun intended... The geometric mean of 2 and 54 is square root of 108.