Sequences — GCSE Mathematics Revision
Revise Sequences for GCSE Mathematics. Step-by-step explanation, worked examples, common mistakes and exam-style practice aligned to AQA, Edexcel, OCR, WJEC, Eduqas, CCEA, Cambridge International (CIE), SQA, IB, AP.
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- Sequences in GCSE Mathematics: explanation, examples, and practice links on this page.
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Go to Nth Term of Linear SequencesWhat is Sequences?
A sequence is an ordered list of numbers that follows a rule. Arithmetic sequences have a constant difference between terms. Geometric sequences have a constant ratio. You need to find the next terms, describe the rule, and use the nth term formula. The nth term of an arithmetic sequence is a + (n-1)d, where a is the first term and d is the common difference.
Step-by-step explanationWorked example
Find the nth term of 5, 8, 11, 14, ... Common difference d = 3. Using the formula: nth term = 3n + 2. Check: 1st term = 3(1) + 2 = 5. ✓
Mini lesson for Sequences
1. Understand the core idea
A sequence is an ordered list of numbers that follows a rule. Arithmetic sequences have a constant difference between terms.
Can you explain Sequences without copying the notes?
2. Turn it into marks
Find the nth term of 5, 8, 11, 14, .
Underline the method, evidence, or command-word move that would earn credit in GCSE Algebra.
3. Fix the likely mark leak
Watch for this mistake: Confusing the common difference with the first term when writing the nth term.
Write one correction rule before doing another practice question.
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Sequences practice questions
These are original StudyVector questions for revision practice. They are not official exam-board questions.
Question 1
In one GCSE sentence, explain what Sequences is testing.
Answer: A sequence is an ordered list of numbers that follows a rule. Arithmetic sequences have a constant difference between terms.
Mark focus: Precise definition and topic focus.
Question 2
A student sees a Sequences question but is not sure how to start. What should the first method line establish?
Answer: It should identify the rule, equation, diagram feature, or transformation before any calculation. That protects method marks and makes later checking easier.
Mark focus: Method selection and command-word control.
Question 3
A student makes this mistake: "Confusing the common difference with the first term when writing the nth term." What should their next repair task be?
Answer: Do one Sequences question and review the mistake type.
Mark focus: Error correction and next-step practice.
Sequences flashcards
Core idea
What is the main idea in Sequences?
A sequence is an ordered list of numbers that follows a rule. Arithmetic sequences have a constant difference between terms.
Common mistake
What mistake should you avoid in Sequences?
Confusing the common difference with the first term when writing the nth term.
Practice
What is one useful practice task for Sequences?
Answer one Sequences question and review the mistake type.
Exam board
How should you use board notes for Sequences?
Use your own GCSE specification for exact paper wording and depth.
Common mistakes
- 1Confusing the common difference with the first term when writing the nth term.
- 2Using n instead of (n-1) in the formula — the nth term is a + (n-1)d, not a + nd.
- 3Not checking whether a sequence is arithmetic, geometric, or neither before applying a formula.
- 4Forgetting that the nth term formula gives the general term, not the sum of terms.
Sequences exam questions
Exam-style questions for Sequences with mark-scheme style solutions and timing practice. Aligned to AQA, Edexcel, OCR, WJEC, Eduqas, CCEA, Cambridge International (CIE), SQA, IB, AP specifications.
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Step-by-step method
Step-by-step explanation
4 steps · Worked method for Sequences
Core concept
A sequence is an ordered list of numbers that follows a rule. Arithmetic sequences have a constant difference between terms. Geometric sequences have a constant ratio. You need to find the next terms,…
Frequently asked questions
How do I find the nth term of a linear sequence?
Find the common difference d. The nth term is dn + (first term - d). For example, if the sequence is 5, 8, 11, ... then d = 3 and the nth term is 3n + 2.
What is a quadratic sequence?
A sequence where the second differences are constant. The nth term has the form an² + bn + c. Find a from the second difference, then work out b and c by substituting known terms.