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UCL Online STEP and AEA Preparation Sessions Session 11: Sequences and induction Can you identify all of these sequences? 1, 8, 27, 64, 125,…… 1, 3, 6, 10, 15, 21,….. 1, 1, 2, 3, 5, 8, 13, 21, 34,….. 1, 2, 6, 24, 120, 720,…. As well as discussing sequences in general, this session will cover situations where sequences are defined or properties of sequences are deduced recursively or from one term to the next. This will lead naturally to the idea of proof by induction. General algebraic techniques are usually important in questions about sequences. Proof by induction is one way to prove a statement like “11n – 6 is divisible by 5 for all positive integers n.” Example problem Prove, by induction, that for all positive integers n greater than or equal to 8 there exist non-negative integers x, y such that n = 3x + 5y.