### Geometric Sequences / Progressions

The terms “sequence” and “progression” are interchangeable. A “geometric sequence” is the same thing as a “geometric progression”. This post uses the term “sequence”… but if you live in a place that tends to use the word “progression” instead, it means exactly the same thing. So, let’s investigate how to create a geometric sequence (also known as a geometric progression).

Pick a number, any number, and write it down. For example:

Now pick a second number, any number (I’ll choose 3), which we will call the **common ratio**. Now **multiply **the first number by the common ratio, then write their product down to the right of the first number:

Now, continue multiplying each product by the common ratio (3 in my example) and writing the result down… over, and over, and over:

By following this process, you have created a “Geometric Sequence”, a sequence of numbers in which the ratio of every two successive terms is the same.

### Vocabulary and Notation

In the example above, 5 is the **first term** (also called the starting term) of the sequence or progression. To refer to the first term of a sequence in a generic way that applies to any sequence, mathematicians use the notation

This notation is Continue reading Geometric Sequences and Geometric Series