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.