*A geometric sequence is a set of ordered numbers for which the ratio of successive terms is the same.*

## What is a Geometric Sequence?

In a geometric sequence, the first term is multiplied by a number called the common ratio to create the second term which is multiplied by the common ratio to create the third term and so on.

The common ratio, or , is calculated as follows:

Like in arithmetic sequences, the first term is denoted by .

To find whether a sequence is geometric, *all* terms must be tested for a common ratio. This is calculated as follows:

### Example 1

**Which of the following are geometric sequences?**

**a) **

Check that the ratio is the same.

There is a common ratio of 4. Therefore this is a geometric sequence where and .

**b) **

Check that there is a common ratio.

There is a common ratio of -2. Therefore this is a geometric sequence where and .

**c) **

There is *not* a common ratio so this is *not* a geometric sequence.

#### See also

Finding the Terms of a Geometric Sequence

Sum of a Finite Geometric Sequence

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