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 often labelled or to show their position.
For example, look at this sequence:
Here, , , , and so on. The three dots () tell us the sequence continues.
Think of a sequence like a playlist on your phone — each song has a specific position (track 1, track 2, track 3…) and there's a reason you put them in that order. In maths, the "reason" is a rule that connects the numbers.
Term-to-Term Rules
One way to describe a sequence is by explaining how you get from one term to the next. This is called a term-to-term rule.
A rule that tells you what operation to perform on a term to get the next term in the sequence.
Look at this sequence:
To get from one term to the next, you add 4 each time:
So the term-to-term rule is: "add 4" and the first term is 3.
To fully describe a sequence using a term-to-term rule, you need two pieces of information: the first term and the rule for getting from one term to the next.
Find the next three terms of the sequence:
Step 1: Find the term-to-term rule.
, ,
The rule is subtract 4 (or add ).
Step 2: Apply the rule to find the next terms.
Answer: The next three terms are .
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