Geometric Progressions

## Geometric Progressions

A geometric sequence is based on raising a number to a power, where the power is the term.

This is written as u_n = ar^n, where u_n is the value for the term, a is a constant, and r^n is a number raised to the term.

## Example 1

What are the values for the first four terms in the sequence given by u_n = 0.8^n?

0.81 = 0.8

0.82 = 0.64

0.83 = 0.512

0.84 = 0.4096

## Example 2

In a sequence u_n = r^n, What is the value of the first term in this sequence:

..., 1.44, 1.728, 2.0736, 2.48832 ?

u_2 = r^2

1.44 = r^2

r = 1.2

Check with a subsequence term: 1.23 = 1.728