In mathematics, a sequence is an ordered list of objects in which repetitions are allowed and order matters. In particular, a sequence is a list of things, usually numbers, that are in order. Sequences can be infinite or finite, depending on whether they go on forever or not. Sequences can follow a specific pattern that can be used to extend them indefinitely. For example, the sequence 2, 5, 8 follows the pattern "add 3," and we can continue the sequence by adding 3 to the last term. Sequences can have formulas that tell us how to find any term in the sequence.
There are different types of sequences, including arithmetic, geometric, and harmonic sequences. An arithmetic sequence is a sequence in which every term is created by adding or subtracting a definite number to the preceding number. A geometric sequence is a sequence in which every term is obtained by multiplying or dividing a definite number with the preceding number. A harmonic sequence is a series of numbers that is said to be in harmonic sequence if.
Sequences are useful in a number of mathematical disciplines for studying functions, spaces, and other mathematical structures using the convergence properties of sequences. In particular, sequences are the basis for series, which are important in differential equations and analysis.
