An infinite sequence is an endless progression of discrete objects, especially numbers. It has a clear starting point and is written in a definite order. An infinite sequence may include all the numbers of a particular set, such as all positive integers {1, 2, 3, 4 …}, or it could be an arithmetic sequence or a geometric sequence. An arithmetic infinite sequence is a progression of numbers where the difference between each consecutive term is constant, while a geometric sequence is one where the common ratio is constant.
Infinite sequences are used in mathematics to study the concept of infinity. Mathematicians use various forms of language and symbolism to try to understand something about the elusive concept of infinity. An infinite sequence of numbers may be represented as {a1, a2, a3, … an, a(n+1), …} .
It is important to note that not all lists of numbers are infinite sequences. An infinite sequence is a function with a domain of all positive integers.
