What is an arithmetic sequence?

An arithmetic sequence is a sequence where the difference between one term and the previous term is always the same. So the difference between the 1st and the 2nd term is the same as the difference between the 10th and 11th term. This can be described recursively as equation or explicitly as:

    equation

Example of an arithmetic sequence

Consider the following sequence:

    equation

We can find the difference by subtracting two terms: equation. And indeed the difference between every term is 3. Now, to express this sequence explicitly in the general form given above:

    equation

So to find the 5th element, for example, we get equation. We see that this is the same as the 5th element in the sequence above.