Edexcel International GCSE Mathematics A · 4MA1
Arithmetic sequences
An arithmetic sequence has a constant difference between consecutive terms. The nth-term rule gives a term directly from its position. A term-to-term rule tells you how to move from one term to the next, which is less efficient for distant positions.
Key method
Use uₙ = a + (n − 1)d, where a is the first term and d is the common difference. Position numbers start at 1.
Worked example
Find the nth term and the 20th term of 7, 11, 15, 19, …
- The common difference is 4, so begin with 4n.
- At n = 1, 4n gives 4; add 3 to obtain the first term 7.
- Substitute n = 20 into 4n + 3.
Answer and interpretation
uₙ = 4n + 3 and u₂₀ = 83.
Common mistake
Using 7 + 4n shifts the sequence by one position.
Practise independently
Does 100 occur in this sequence?
Check your answer
4n + 3 = 100 gives n = 24.25, not a positive integer, so no.
Syllabus connection
This lesson develops linear sequences within the algebra area. Start with the worked method, attempt the independent question without looking at its answer, then explain any correction in your own words. Check the official specification for your tier’s full requirements.
Related resources
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