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??

\[U_1 = ...\]

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.




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