An arithmetic sequence, also known as an arithmetic progression, is a sequence of numbers where the difference between any two consecutive terms is constant throughout the sequence. This constant difference is called the common difference of the arithmetic sequence. For example, the sequence 5, 8, 11, 14, 17 is an arithmetic sequence with a common difference of 3.
Arithmetic sequences can be finite or infinite. A finite portion of an arithmetic sequence is called a finite arithmetic progression. The sum of a finite arithmetic progression is called an arithmetic series.
Arithmetic sequences can be defined using the first term and the common difference. If the initial term of an arithmetic sequence is a₁ and the common difference of successive members is d, then the n-th term of the sequence (aₙ) is given by the formula aₙ = a₁ + (n-1)d.
Arithmetic sequences are used in various fields, including mathematics, physics, and computer science. They are also commonly used in financial calculations, such as calculating compound interest.
