The geometric mean is the root of the product of the terms.Question 1
Let be a set of positive numbers in geometric progression.
Suppose is odd.
Show that the geometric mean and the median of are the same.
This is a geometric sequence with first term and common ratio
. . The sequence is: .
The product of the terms is: .
The Geometric Mean is: .
The median is the "middle" term of the sequence: . .