Sequence
In mathematics, a sequence refers to an ordered list of numbers or elements
In mathematics, a sequence refers to an ordered list of numbers or elements. Each element in a sequence is called a term, and the position of a term in the sequence is called its index or subscript.
Sequences can be represented either explicitly or recursively. An explicit representation of a sequence provides a formula or a pattern that directly gives the value of each term based on its position. For example, the sequence of even numbers can be represented explicitly as 2, 4, 6, 8, 10, … with the formula nth term = 2n.
On the other hand, a recursive representation of a sequence defines each term in terms of one or more preceding terms. For example, the Fibonacci sequence is defined recursively as follows: the first two terms are 0 and 1, and each subsequent term is the sum of the two preceding terms. So, the Fibonacci sequence starts as 0, 1, 1, 2, 3, 5, 8, … where each term is the sum of the previous two terms.
Sequences can be finite or infinite. A finite sequence has a specific number of terms, while an infinite sequence continues indefinitely without ending.
Sequences are widely used in various branches of mathematics, including calculus, number theory, and statistics. They provide a framework to study patterns, make predictions, and analyze mathematical structures.
More Answers:
Multiplying 9 by 2 | The solution and explanation for 9×2.Simplifying the Expression 10×2 | Multiplying 10 by 2 Equals 20
Unveiling the Power of Patterns | Exploring Mathematical Concepts in Numbers, Shapes, and Functions