What is a Sequence?

A sequence is a collection of numbers or objects arranged in a particular order following a specific rule or pattern. Each element in a sequence is called a term. Sequences are commonly used in mathematics to study the behavior of a series of numbers or to identify patterns that help in solving mathematical problems.

Types of Sequences:

There are several types of sequences, some of the common ones are:

• Arithmetic Sequences: In an arithmetic sequence, each term is found by adding a constant value to the previous term.
• Geometric Sequences: In a geometric sequence, each term is found by multiplying the previous term by a fixed value.
• Fibonacci Sequence: In the Fibonacci sequence, each term is the sum of the two preceding terms, starting with 0 and 1.

Notation:

Sequences can be represented using a notation where the position of a term is denoted by subscripts. For example, in a sequence {1, 3, 5, 7, 9, ...}, the terms can be represented as a₁, a₂, a₃, a₄, a₅, ... where a₁ = 1, a₂ = 3, a₃ = 5, and so on.

Overall, sequences play a vital role in mathematics and are used in various mathematical concepts and calculations.