GCSE Mathematics · Edexcel 1MA1 · Topic A.4
Sequences
Key points
- An arithmetic sequence goes up or down by the same amount each time. Its nth term is , where is the common difference and the first term, e.g. 5, 8, 11, ... has nth term .
- To test whether a number is in a sequence, set the nth term equal to it and check whether is a whole number.
- A geometric sequence multiplies by the same ratio each time, e.g. 3, 6, 12, 24 (ratio 2).
- Fibonacci-type sequences add the previous two terms.
- Know special sequences: square numbers, cube numbers and triangular numbers (1, 3, 6, 10, ...).
- Quadratic sequences (higher) have a constant second difference; the coefficient is half the second difference, e.g. 2, 6, 12, 20 has nth term .
Topic notesPremium
A sequence is an ordered list of numbers that follows a rule. You need to continue sequences, find and use an nth term formula, recognise special sequences and, at Higher tier, find the nth term of a quadratic sequence.
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