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, 21ā¦ 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 Ć· 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 ā 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 ā if they are not constant, check the ratios instead
- Fibonacci errors: Each term is the SUM of the two before it ā 1, 1, 2, 3, 5, 8ā¦ ā do not add three terms or multiply
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.
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
What is a sequence in maths?
A list of numbers that follow a rule or pattern. Each number in the list is called a term.
What is a term in a sequence?
Each individual number in the sequence. The 1st term is denoted T(1) or uā, the 2nd term is T(2), etc.