Lecture Notes on Sequences, Recurrence, and Difference Equations

These flashcards cover key terms and concepts from the lecture on sequences, recurrence relations, and difference equations.

Sequence

A function whose domain is the set of natural numbers and whose range is the set of real numbers.

Converge

A sequence converges to L if the limit of the sequence approaches L as n approaches infinity.

Diverge

A sequence diverges if it does not have a finite limit.

Difference Equation

An equation that relates a sequence with its predecessors.

Order of Difference Equation

The number of previous terms needed to compute the current term in a difference equation.

Recurrence Relation

A type of equation that defines each term of a sequence in terms of previous terms.

Exponential Sequence

A sequence where each term is an exponential function of n, e.g., an = 2n.

Oscillatory Sequence

A sequence that fluctuates but does not converge to a limit.

Limit of a Sequence

The value that a sequence approaches as the index approaches infinity.

Population Doubling

A model where the population increases by a fixed factor in each time period.