A number sequence is a list of numbers arranged in a specific order following a particular rule or pattern. Examples include arithmetic sequences where each term increases or decreases by a constant value and geometric sequences where each term is multiplied by a fixed number.

Patterns in mathematics help identify regularities in numbers shapes and arrangements. These patterns can be numerical geometric or logical. Recognizing these patterns improves problem-solving and logical thinking. It also helps students predict future terms in sequences and understand complex mathematical concepts more easily which is crucial for higher-level math learning.