Knowledge Organiser: Sequences
Part of Sequences · GCSE GCSE Mathematics revision
This topic summary covers Knowledge Organiser: Sequences within Sequences for GCSE Mathematics. Revise Sequences in Algebra for GCSE Mathematics with 14 exam-style questions and 12 flashcards. This is a high-frequency topic, so it is worth revising until the explanation feels precise and repeatable. It is section 7 of 7 in this topic. Use this topic summary to connect the idea to the wider topic before moving on to questions and flashcards.
Topic position
Section 7 of 7
Practice
14 questions
Recall
12 flashcards
Knowledge Organiser: Sequences
Key Terms
- Sequence: An ordered list of numbers following a rule
- Term: Each number in a sequence (1st term, 2nd term, etc.)
- Common difference: The fixed amount added/subtracted in an arithmetic sequence
- Arithmetic sequence: Adds/subtracts the same value each time
- Geometric sequence: Multiplies/divides by the same value each time
- Fibonacci sequence: Each term is the sum of the two previous terms
Must-Know Facts
- To find the next term: apply the same rule to the last known term
- Arithmetic: differences between consecutive terms are constant
- Geometric: ratios between consecutive terms are constant
- Fibonacci: 1, 1, 2, 3, 5, 8, 13, 21… each term = sum of previous two
- A sequence can be described by a term-to-term rule or a position-to-term rule
- Check your rule generates the given terms before using it
Key Methods
- Arithmetic: find the common difference; check it's constant
- Geometric: find the common ratio (term ÷ previous term); check it's constant
- Describe: state the first term and the term-to-term rule
- Generate terms: start from the first term and apply the rule repeatedly
Common Mistakes
- Confusing arithmetic and geometric sequences: Arithmetic sequences add a fixed amount; geometric sequences multiply by a fixed ratio — check which operation links consecutive terms
- Applying the rule to the wrong term: Always apply the term-to-term rule to the LAST known term, not to the term number
- Describing a geometric sequence as arithmetic: Check the differences — if they are not constant, check the ratios instead
- Fibonacci errors: Each term is the SUM of the two before it — 1, 1, 2, 3, 5, 8… — do not add three terms or multiply
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Read this section alongside the surrounding pages in Sequences. That gives you the full topic sequence instead of a single isolated revision point.
Practice Questions for Sequences
What is the common difference of the arithmetic sequence below? 4, 11, 18, 25, 32, ...
Zara says: 'The sequence 4, 12, 36, 108 is an arithmetic sequence.' Explain why Zara is wrong. State what type of sequence it actually is.
Quick Recall Flashcards
14 questions on Sequences — practise free
Instant marking, adaptive difficulty, and 12 spaced repetition flashcards. Free until your GCSEs.
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