A Sequence is a set of things (usually numbers) that are in order.

In a Geometric Sequence, each term is found by multiplying the previous term by a constant (called “common ratio”).

Example: 2, 4, 8, 16, 32, 64, 128, 256, ...

Suppose in a geometric sequence:

• a is the first term, and
• r is the common ratio

Then the n_th term in the geometric sequence is: ar^n-1

The sum of the geometric sequence is:

Another related concept is geometric mean. Geometric mean of a collection of n positive real numbers is the nth root of the product of the numbers.

For example: The geometric mean of the numbers 2 & 8 is sqrt(2*8) = 4.

In the geometric sequence above, 2, 4, 8 forms a geometric sequence, and the middle number, 4, is the geometric mean of 2 and 8.