Sequences are ordered arrangements of numbers or objects from "summary" of Maths Mate – 6 NEW by Madhubun
A sequence is a set of numbers or objects that are arranged in a specific order. In a sequence, the position of each number or object matters, as the order is crucial. This means that if the numbers or objects are rearranged, the sequence changes. Each element in a sequence is called a term, and the position of each term in the sequence is known as its term number.
Sequences can be classified based on their patterns or relationships between the terms. Some sequences follow a specific rule or formula, while others may not have a clear pattern. Arithmetic sequences, for example, have a common difference between consecutive terms, while geometric sequences have a common ratio between consecutive terms. These patterns help us predict future terms in the sequence and understand the relationship between the terms.
Sequences can be represented in various ways, such as using tables, graphs, or algebraic expressions. Tables display the terms of the sequence in a tabular format, making it easy to identify the pattern. Graphs represent the terms of the sequence on a coordinate plane, showing how the terms change over time. Algebraic expressions provide a formula to calculate any term in the sequence based on its position.
Understanding sequences is essential in mathematics as they appear in various contexts, such as number patterns, functions, and series. By studying sequences, we can develop problem-solving skills, logical reasoning, and critical thinking. Sequences play a vital role in mathematics and have practical applications in various fields, including science, engineering, and computer science. By exploring the patterns and relationships in sequences, we can uncover hidden connections and make sense of the world around us.
