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.

Example:

1, 2, 4, 8, 16, 32, 64, 128, 256, ...

In General we write a Geometric Sequence like this:

{a, ar, ar2, ar3, ... }

We can also calculate any term using the Rule:

xn = ar(n-1)

(We use "n-1" because ar0 is for the 1st term)

Example,

10, 30, 90, 270, 810, 2430, ...

The values of a and r are:

  • a = 10 (the first term) 
  • r = 3 (the "common ratio")

The Rule for any term is:

xn = 10 × 3(n-1)