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Geometric Mean

☼ Geometric Mean : The geometric mean (G.M.) of n numbers is the nth root of the product of the n numbers.

Therefore, Geometric mean of $a_{1},a_{2},a_{3},...,a_{n}$ is = G. M. = $\sqrt[n]{a_{1},a_{2},a_{3},...,a_{n}}$

e.g. Find the geometric mean of 9, 12 and 16.

Soln. G.M. = $\sqrt[3]{9\times 12 \times 16}$ = $\sqrt[3]{3\times 3\times 4\times3 \times4 \times 4}$ = 3 $\times$ 4 = 12.