Sequences

**Sequences**

A **sequence** is an ordered set. It may be finite or infinite. Many times a sequence will follow a pattern. If you add a constant amount to each term in order to find the next term, you are working with an **arithmetic sequence**.

What value is being added to each number in this sequence?

**...-5, -3, -1, 1, 3, 5 ...**

+2 is the constant value that is being added to each number in the sequence. It is also called the common difference, and is denoted by the variable "*d*."

Why is it called the common *difference*?

If you look at the terms working backwards, you will see that the difference between term 6 and term 5 is +2; the difference between term 5 and term 4 is +2; the difference between term 3 and term 2 is +2, and so on. Thus the common difference for this sequence is +2.

A common difference is not the only relationship that numbers in a sequence can have. You'll notice other patterns. They may simply involve multiplication or division, or they may be governed by an algebraic expression, a.k.a. "**rule**" or "**general term**."

You will often see the following notation:

The sequence can then be evaluated for a specific term, *n*, by inputting the value of *n* into the expression.

You may also be asked to derive the formula, or rule, from a given sequence. When you do this, you will have "produced the general term of the sequence."