Sequences Vocabulary

Flashcards on Sequences based on lecture notes.

Sequence

A sequence is a list of numbers: a1, a2, a3, . . .

General Term

Also known as the nth term, it describes the formula to find any element in the sequence.

Finite Sequence

Sequences with a limited number of terms.

Infinite Sequence

Sequences with an endless number of terms.

Decreasing Sequence

A sequence where an+1 < an for every n.

Increasing Sequence

A sequence where an+1 > an for every n.

Monotonic Sequence

A sequence that is either decreasing or increasing.

Bounded Below Sequence

There exists a number m such that an ≥ m for every n; m is a lower bound.

Bounded Above Sequence

There exists a number M such that an ≤ M for every n; M is an upper bound.

Bounded Sequence

A sequence that is both bounded below and bounded above.

Arithmetic Sequence

A sequence where the difference between consecutive terms is constant: an+1 − an = constant.

Geometric Sequence

A sequence where the ratio between consecutive terms is constant: an+1 / an = constant (non-zero).

Limit of a Sequence

A real number A such that an approaches A as n approaches ∞. Represented as lim n→∞ an = A.

Convergent Sequence

A sequence that has a limit.

Divergent Sequence

A sequence that does not have a limit.

Big O Notation

Used in Computer Science to describe the complexity of an algorithm; O(nk) denotes a class of functions for which lim n→∞ f(n)/nk = C, where C is a non-zero constant.