9.3 - Geometric Sequences

Geometric Sequences are sequences that have a common ratio (r).

Or...

A simple form of a Geometric Sequence

A popular example is

1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, ...

Every consecutive term is 2 times the preceding term.

In this particular sequence, a=1 and r=2

The Sum of a Finite Geometric Sequence can be defined under this equation:

If you were to plug in the previous sequence you'd get:

And, finally, the Sum of an Infinite Geometric Sequence

IMPORTANT:  This formula only works if  | r | < 1

The formula is simply: