9.2: Arithmetic Sequences & Partial Sums

As defined by the book, a sequence is arithmetic if the differences between consecutive terms are the same.

The common difference, or d, is the difference between each number in an arithmetic sequence.

An example of an arithmetic sequence would be something like this:

3, 5, 7, 9, 11, 13, 15, ...

This sequence has a common difference is 2.

There are a few equations that go along with arithmetic sequences and this section.                                                         First is the explicit formula:
                                  

         

Next is the recursive formula:

To find the nth term of an arithmetic sequence, use the formula:

Last is the formula to find the partial sum (the sum of the terms in a sequence):

I think that's about it for arithmetic sequences! And remember, never go in against a Sicilian, when death is on the line!

Jessica