Introduction

Video lesson

A recurrence relation is a type of recursive sequence which relies on knowing the previous term in order to obtain the next consecutive term.

i.e. if we wanted to know the $100^{th}$ term in a sequence, we would need to know the first 99 terms.

e.g. For the sequence 1, 5, 9, 13, ...

$U_0 = 1$ where $U_0$ is the initial term in the sequence.

Rule: add 4 to previous term

i.e. $U_{n+1} = U_n + 4$

An example of a recurrence relation is gaining compound interest on money in a bank account.

You invest £100 in a bank account with an interest rate of 2%.

i.e. $U_{n+1} = 1.02U_n, \ U_0 = 100$ where $U_n$ is the amount in the bank account after $n$ years.

$u_0$ or $u_1$ ? read which term the sequence starts from. Being one term out runs through the entire rest of the question.
Each term depends on the one before: you cannot jump to the tenth term without generating the ones in between, unless a formula is given.
Keep full accuracy: rounding each term compounds the error quickly. Carry the decimals through.
Read the context carefully: "10% is removed" means multiplying by 0.9, not subtracting 10.