Number sequences are lists of numbers arranged in a specific order following a 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. Sequences are essential in understanding mathematical relationships.

Patterns in mathematics involve recognizing regularities in numbers shapes and arrangements. These patterns can be numerical geometric or logical. Identifying patterns enhances problem-solving skills and logical thinking. It helps predict the next terms in sequences and understand mathematical concepts which are essential for mastering higher-level math and its applications.