Arithmetic sequences

An arithmetic sequence is a sequence of numbers in which the difference between consecutive terms is constant.

That means that each term is more than the last term.

For example, the sequence:

is an arithmetic sequence where each term is 3 more than the previous term.

The constant difference between the terms is called the “common difference”.

Form of an arithmetic sequence

Arithmetic sequences can be written in the form:

Where:

This form is known as the “nth term” of the sequence.

To find the nth term of a sequence, we need to find two things:

Once we’ve found these, just substitute and into the formula !

To find the common difference, simply subtract any term from the term after it.

For example, in the sequence:

The common difference is , because, for example, .

The offset () can be found by subtracting the common difference from the first term.

For example, in the sequence:

The common difference is , and the first term is , so the offset is: