What is a Sequence?
A sequence is an ordered list of numbers that follow a particular pattern or rule. Each number in a sequence is called a term.
An ordered list of numbers that follow a specific pattern or rule.
Each individual number in a sequence. Terms are usually labelled by their position: 1st term, 2nd term, 3rd term, and so on.
Here are some examples of sequences:
- 2, 4, 6, 8, 10, ... (even numbers)
- 5, 10, 15, 20, 25, ... (multiples of 5)
- 3, 7, 11, 15, 19, ... (adding 4 each time)
- 1, 2, 4, 8, 16, ... (doubling each time)
The three dots "..." at the end mean the sequence continues forever — it doesn't stop!
Think of a sequence like a chain of beads on a necklace. Each bead is a term, and the pattern you use to pick the next bead is the rule. If you know the rule, you can always figure out what bead comes next!
The Term-to-Term Rule
The term-to-term rule tells you how to get from one term to the next. It describes what you do to any term in order to find the term that comes right after it.
A rule that describes the operation you perform on one term to get the next term in a sequence.
To find the term-to-term rule, look at what happens between consecutive terms:
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3, 7, 11, 15, 19, ...
- , ,
- Term-to-term rule: add 4
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20, 17, 14, 11, 8, ...
- ,
- Term-to-term rule: subtract 3
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2, 6, 18, 54, ...
- , ,
- Term-to-term rule: multiply by 3
To find the term-to-term rule, always check the difference (or ratio) between consecutive terms. If the difference is the same each time, you have a constant term-to-term rule.
The term-to-term rule only works well if you know the previous term. If someone asks you for the 100th term, you'd need to work through all 99 terms before it — that's a LOT of work! That's why we also learn the nth term rule.
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