The GM of the terms is equal to the square root of the product of the first and last terms: $\sqrt{a \cdot (ar^{n-1})} = a r^{\frac{n-1}{2}}$.

The GM of the terms is equal to the median of the terms if $n$ is odd.

The GM of the terms is equal to the arithmetic mean of the middle two terms if $n$ is even.

The logarithm of the GM of the terms is equal to the arithmetic mean of the logarithms of the terms.