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. The first term of an arithmetic sequence is denoted by "a" and the common difference is denoted by "d". The nth term of an arithmetic sequence can be found using the formula: a + (n-1)d.
Arithmetic sequences can be finite or infinite. A finite portion of an arithmetic sequence is called a finite arithmetic progression, and the sum of a finite arithmetic progression is called an arithmetic series. The sum of the members of a finite arithmetic progression can be found using the formula: (n/2)(a + l), where n is the number of terms, a is the first term, and l is the last term.
Arithmetic sequences are used in various fields, including mathematics, physics, and computer science. They are also commonly used in everyday life, such as in calculating interest rates on loans or mortgages.
