Question

find the geometric mean.
8,_, 72
explain please.

Answer 1

If this thing is growing at a constant geometrical rate, then letting your unknown be x, you have\[\frac{x}{8}=\frac{72}{x} \rightarrow x^2=72 \times 8 =576 \rightarrow x=\sqrt{576}=24\]here.

To find the geometric mean, you multiply every element in the sequence and raise it to the power of 1/(no. of elements), so here:\[\mu = (8 \times 24 \times 72)^{1/3}=24\]as required.