GE 103 – Mathematics in the Modern World - Unit II: The Types of Sequence

Vocabulary flashcards covering the definitions, formulas, and fundamental concepts of mathematical sequences including Arithmetic, Geometric, Harmonic, and Fibonacci sequences.

Sequence

An ordered list of numbers that follows a specific rule or pattern.

Term

Each individual number within a mathematical sequence.

$$a_1$$

The notation used to represent the first term of a sequence.

Arithmetic Sequence

A sequence where the difference between consecutive terms is constant.

Common Difference ($d$)

The constant value representing the difference between consecutive terms in an arithmetic sequence.

Arithmetic Sequence Formula

The formula used to find the nth term: $a_n = a_1 + (n - 1)d$.

Geometric Sequence

A sequence formed by multiplying each term by the same number, known as the common ratio.

Common Ratio ($r$)

The constant number multiplied by each term in a geometric sequence to obtain the subsequent term.

Geometric Sequence Formula

The formula used to find the nth term: $a_n = a_1(r)^{n - 1}$.

Harmonic Sequence

A sequence formed when the reciprocals of the terms form an arithmetic sequence.

Fibonacci Sequence

A sequence in which each term is obtained by adding the previous two terms.