Consider the sequence 2, 5, 8, . . . How would you describe how to calculate the next term from the previous term?

Each term in this sequence is 3 more than the term before it.

Here is a way to describe this sequence: the starting term is 2, and the .

This is an example of an arithmetic sequence. An arithmetic sequence is a sequence in which the value of each term is the value of the previous term added to a constant. If we know the constant to add, we can use it to find other terms.

For example, each term in this sequence is 3 more than the term before it. To find this constant, sometimes called the rate of change or common difference, we can subtract consecutive terms. This can also help us decide whether a sequence is arithmetic.

For example, the sequence 3, 6, 12, 24 is not an arithmetic sequence because . But the sequence 100, 80, 60, 40 is arithmetic because the differences of consecutive terms are all the same: . This means that the rate of change is -20 for the sequence 100, 80, 60, 40.

It is important to remember that, while the last two lessons have introduced geometric and arithmetic sequences, there are many other sequences that are neither geometric nor arithmetic.