What is a Sequence?
Sequence: An ordered list of items , numbers, shapes, letters, or objects , that follow a predictable rule.
Term: Each individual item in a sequence is called a term. Terms are usually labelled by their position: the 1st term, 2nd term, 3rd term, and so on.
Sequences appear everywhere in mathematics. Here are a few examples:
- 2, 5, 8, 11, 14, ... , each term increases by 3
- 100, 50, 25, 12.5, ... , each term is halved
- 🔴, 🔵, 🔴, 🔵, ... , colours alternate in a pattern
The key idea is that there is always a rule connecting the terms , nothing is random!
Think of a sequence like a playlist on shuffle... except it's not on shuffle. Every song (term) follows a specific order decided by one clear rule. If you know the rule, you can predict every song that comes next.
Patterns in Sequences
Pattern: A set of items or numbers that follow a predictable rule. In algebraic patterns, the same mathematical procedure , such as adding, subtracting, multiplying, or dividing , is applied each time to get the next term.
Patterns can involve:
- Addition , adding the same number each time (e.g. +3, +5, +10)
- Subtraction , decreasing by the same amount each time (e.g. −6, −4)
- Multiplication , multiplying by the same number each time (e.g. ×2, ×10)
- Division , dividing by the same number each time (e.g. ÷10, ÷3)
- Combinations , sometimes more than one operation is used
When the difference between consecutive terms is always the same, the pattern is called a linear pattern. For example, 3, 7, 11, 15, ... has a constant difference of +4, so it is linear.
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