Mathematical Problems Involving Patterns

Flashcards covering key terms and definitions related to mathematical problems involving patterns.

Pattern

A repeated arrangement of numbers, shapes, colors, or designs, related to any type of event or object characterized by a specific rule.

Sequence

A succession of numbers in a specific order.

Term

Numbers in a sequence, such as the 1st term, 2nd term, etc.

Finite Sequence

A sequence that has a first term and a last term, leading to a limited domain.

Infinite Sequence

A sequence that has no end, indicated by an ellipsis, representing an unlimited domain.

General Term (nth term)

The function value of a sequence denoted by a(n).

Arithmetic Sequence

A sequence in which each term after the first differs from the preceding term by a constant, called the common difference.

Common Difference (d)

The difference between consecutive terms in an arithmetic sequence.

Geometric Sequence

A sequence where each term after the first is obtained by multiplying the preceding term by a nonzero constant, known as the common ratio.

Harmonic Sequence

A sequence where the reciprocals of the terms form an arithmetic sequence.

Fibonacci Sequence

A sequence where each element is obtained by adding the two preceding elements, starting with 0 and 1.

Golden Ratio (φ)

An irrational number approximately equal to 1.618, related to the Fibonacci sequence and characterized by converging ratios of consecutive Fibonacci numbers.