in mathematics, ordered set of mathematical quantities called terms. A sequence is said to be known if a formula can be given for any particular term using the preceding terms or using its position in the sequence. For example, the sequence 1, 1, 2, 3, 5, 8, 13,… (the Fibonacci sequence) is formed by adding any two consecutive terms to obtain the next term. The sequence − 1 / 2, 1, 7 / 2, 7, 23 / 2, 17,… is formed according to the formula (n²−2)/2 for the nth, or general, term. A sequence may be either finite, e.g., 1, 2, 3,…50, a sequence of 50 terms, or infinite, e.g., 1, 2, 3,…, which has no final term and thus continues indefinitely. Special types of sequences are commonly called progressions. The terms of a sequence, when written as an indicated sum, form a series; e.g., the sum of the sequence 1, 2, 3,…50 is the series 1+2+3+…+50.

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