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 and OCR.
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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. ✓
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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 and OCR 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.