Geometric Series

Key points

A geometric series is the sum of the terms in a geometric sequence.
- There are two types of series – finite and infinite.
There are two main formulae for the sum of n terms of a finite geometric series.
There is one formula for the sum of n terms of an infinite geometric series.
- If the common ratio is greater than one, then the value of the series is infinity.

A geometric series is the sum of the terms in a geometric sequence. A general model of a geometric series is seen to the right.

A finite geometric series is the sum of the terms of a geometric sequence to a given number of terms.
An infinite geometric series is the sum of all of the terms in an geometric sequence to infinity.

Formula Booklet

There are two main formulae used to find the value of a finite geometric series. They are seen to the left.

This formula is used for the sum of n terms of a geometric series.
The formulae are variations of each other, and are essentially the same.
In these formulae, the common ratio cannot be equal to 1 because you would be dividing by 0.
- Any geometric sequence with a common ratio of 1 would just be constant.

There is one formula used to for an infinite geometric series. It is seen to the right.

To use this formula, the absolute value of the common ratio must be less that one.
- In other words, the common ratio must be a decimal. It can be either positive or negative.
- If the common ratio is a decimal, you are dividing between terms, to the point where each term is basically 0, at which point you would no longer be adding anything.
- If the common ratio is greater than one, the terms you are adding keep getting larger, so the sum would be infinite.

Formula Booklet