Maths - Recurrence Relations
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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 $n \in N$.