Sequences of Numbers

A sequence is a list of numbers in a specific order. Each number in the sequence is called a term. The position of a term in the sequence is called its term number.

Types of Sequences

There are different types of sequences:

Arithmetic Sequence: In an arithmetic sequence, each term is obtained by adding a constant value to the previous term. The constant value is called the common difference.
Geometric Sequence: In a geometric sequence, each term is obtained by multiplying the previous term by a constant value. The constant value is called the common ratio.
Fibonacci Sequence: The Fibonacci sequence is a series of numbers in which each number is the sum of the two preceding ones, usually starting with 0 and 1.

Notation

Sequences can be expressed using notation. For example, the nth term of an arithmetic sequence can be represented as: a_n = a₁ + (n-1)d, where a_n is the nth term, a₁ is the first term, and d is the common difference.