What is a sequence?
A sequence is a list of numbers that follow a rule from one term to the next.
A sequence is just an ordered list of numbers. Each number in the list is called a term, and each term has a position — first, second, third, and so on. The first term is usually labelled or , the second , the third , and the term in position is written .
The rule that ties a sequence together can be described two ways. A term-to-term rule says how to get from one term to the next, like "add " or "double then subtract ". A position-to-term rule (also called the nth-term rule) gives any term directly from its position, like .
For the sequence the term-to-term rule is "add ", and the position-to-term rule is . Both describe the same pattern, but the nth-term rule is more useful when you need a far-off term like — no need to add ninety-nine times!
- A sequence is an ordered list of numbers called terms.
- Each term has a position; the term in position is .
- A term-to-term rule jumps from one term to the next.
- A position-to-term rule gives any term directly from .