# Maths - Recurrence Relations

> Source: https://ollybritton.com/notes/a-level/maths/topics/recurrence-relations/ · Updated: 2021-10-09 · Tags: school, maths, sequences, safe-to-post-online

## See Also
- [Maths - Series](https://ollybritton.com/notes/a-level/maths/topics/series/)
- [Further Maths - Series](https://ollybritton.com/notes/a-level/further-maths/topics/series/)

## Flashcards
##### What is a recurrence relation??
A definition of a sequence that depends on the previous terms.

##### If you specify $$U_{k+1} = U_k + 7$$ what must you also specify for it to define a sequence??
$$
U_1 = ...
$$

##### What does it mean for a recurrence relation to be decreasing in terms of $U_{n + 1}$ and $U_n$??
$$
U_{n + 1} < U_n
$$

##### What does it mean for a recurrence relation to be increasing in terms of $U_{n + 1}$ and $U_n$??
$$
U_{n + 1} > U_n
$$

##### What does it mean for a sequence to be periodic??
The terms repeat in a cycle.

##### What is the informal definition of the order of a periodic sequence??
The amount of terms between repeats.

##### What is the formal definition of the order of a periodic sequence??
The value of $k$ where

$$
U_{n + k} = U_n
$$

for all $n \in N$.

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