9.2 Arithmetic Sequences

A sequence is arithmetic if the difference between consecutive terms is the same each time.
Arithmetic sequences have a common difference (d).
This means that:



An example of an arithmetic sequence would be
4,6,8,10,...

In this example, the common difference is 2.

The explicit formula for an arithmetic sequence is

The recursive formula for the previous example (4,6,8,10,...) would be

The sum of a finite arithmetic sequence is

Using the 4,6,8,10,... sequence with n=6, the sum would equal

= 54