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This lesson covers Sequences and Series as required by the A-Level Mathematics Pure 1 specification. A sequence is an ordered list of numbers following a rule, and a series is the sum of the terms of a sequence. This topic includes arithmetic and geometric sequences, sigma notation, the binomial expansion, and recurrence relations.
An arithmetic sequence has a constant difference between consecutive terms. This difference is called the common difference d.
| Formula | Description |
|---|---|
| uₙ = a + (n − 1)d | nth term |
| Sₙ = n/2 × (2a + (n − 1)d) | Sum of first n terms |
| Sₙ = n/2 × (a + l) | Sum using first and last terms |
where a is the first term, d is the common difference, and l is the last term.
Example: The 5th term of an arithmetic sequence is 17 and the 12th term is 38. Find a and d.
u₅ = a + 4d = 17
u₁₂ = a + 11d = 38
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