4.2

True or false: some sequences are most naturally defined by specifying one or more initial terms than giving a rule for determining subsequent terms from earlier terms in a sequence

true

recurrence relation

a rule that defines a term avn as a function of previous terms in the sequence

what is the general recurrence relation for an arithmetic sequence?

avn = av n-1 + d (d being the recursive rule)

what is the general recurrence relation for a geometric sequence?

avn = av n-1 * r

What is the recurrence relation for the Fibonacci sequence?

avn = fv n-2 + fv n-1

The number of initial values required to define a sequence using a recurrence relation depends on ____

which previous terms in the sequence are used in the recursive rule

Dynamical system

A system in which the state of the system at any point in time is determined by a set of well defined rules that depend on the past states of the system

Discrete time dynamical system

time is divided into discrete intervals

ex. balance of interest earning account (what is the balance on an account that earns 2% annual interest compounded quarterly?)