If you add up all the terms of an arithmetic sequence, you have an arithmetic series. For instance,

There is a “trick” that can be used to add up the terms of any arithmetic series. While this trick may not save much time with a 6-item series like the one above, it can be very useful if adding up longer series. The trick is to work *from the outside in*.

Consider the example given above:

Pause here and check the following things.

- You understand the calculation that was done for this particular example.
- You understand that this “trick” will work for any arithmetic series.
- You understand that this trick will
*not*work, in general, for series that are not arithmetic.

If we apply this trick to the *generic* arithmetic series, we get a formula that can be used to sum up any arithmetic series.

Every arithmetic series can be written as follows:

If you add the first and last terms, you get

Comments:"DAISY and BRF versions of this collection are available."