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Geometric mean of 2 and 12 is 4.898979485566356. Look at 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.
The geometric mean of two numbers is the square root of their product. For example, the geometric mean of 4 and 25 is 10.
Neither.