Chapter 15

# Going Out of Sequence with Sequences and Series

In This Chapter

Working with sequences and their terms

Recognizing arithmetic and geometric patterns

Examining recursive sequences: Going back two or more terms

Summing up the terms in a sequence with a series

A *sequence* is a list of items all separated by commas (milk, sugar, eggs … okay, so it’s generally a list of numbers). Mathematical sequences usually have a rule determining what number comes in which position in the list. A *series* is the sum of the numbers in a sequence — or that list. You add up a few or many or all the terms in a sequence.

In this chapter, you see arithmetic and geometric sequences — some of the more commonly used sequences. You also form many other types of sequences by just writing a rule using various mathematical operations. Finally, you figure out how to add the terms in a sequence using rules that apply to series.

## Writing the Terms of a Sequence

The sequence 1, 3, 5, 7, 9, … consists of the odd positive integers. Notice that I stop listing the numbers at 9, hoping that you can determine the ...