Lecture 16 - Sequences & Summations

These flashcards cover key vocabulary terms related to Logic and Algorithms, specifically focusing on sequences and summations.

Sequence

A function whose domain is a subset of integers.

Term of a sequence

The expression an represents a sequence, where n is the index.

Explicit formula

An equation that defines the n^th term of a sequence directly, such as a_n = 2n + 1.

Recursive definition

A way to define a sequence using initial term(s) and a recurrence relation.

Geometric sequence

A sequence where each term is found by multiplying the previous term by a constant, known as the common ratio.

Arithmetic sequence

A sequence where each term is found by adding a constant, known as the common difference, to the previous term.

Summation notation

A mathematical notation used to express the sum of terms in a sequence.

Index of summation

The variable used in summation notation, which often represents the position of a term in the sum.

Closed form

An expression that provides an exact value of a summation without using summation notation.

Recurrence relation

A formula that relates each term in a sequence to one or more of its predecessors.