Unit 3
Repeating Pattern Sequence
About this unit
Identify the repeating cycle or growth rule in number, shape, and symbol sequences — then use it to find any term, no matter how far along the sequence. This unit also covers growing patterns where you need to find a formula for the nth figure.
What types of questions will you face?
- 1Find the element at a large position (e.g. 999th, 1004th) in a repeating symbol or number cycle
- 2Calculate how many elements (cubes, circles, matchsticks) will be in figure N of a growing pattern
- 3Identify the rule operating in an arithmetic or geometric number sequence
- 4Work out the position of a specific element within a pattern diagram
- 5Decode rule-based sequences where the rule toggles or transforms a state
Skills you will build
- Finding the cycle length of a repeating sequence
- Using division with remainder (modular arithmetic) to locate the nth term
- Identifying and extending linear and quadratic growing patterns
- Recognising Fibonacci, triangular, and other classic sequences
- Translating a visual pattern into a numerical formula
By the end of this unit, you will be able to
- Find the element at any position in a repeating sequence in seconds using remainders
- Generate a formula for how many elements will be in the nth figure of a growing pattern
- Recognise common sequence types and apply the right rule immediately
- Decode complex toggle-based or rule-based state sequences
Difficulty profile
Ranges from Very Easy (simple repeating cycles) to Difficult (complex growing patterns with combined rules). The Fibonacci sequence and toggle-based puzzles are the hardest questions in this unit.
Exam tip: Repeating Pattern Sequence
For repeating sequences: count the cycle length (e.g. 8 symbols), divide the position by that length, and the remainder tells you which symbol it is. If remainder = 0, it's the last in the cycle.
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