Sequences definitions Flashcards
Sequences definitions
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Sequence An ordered list of numbers where each entry follows a specific pattern or rule, often described by a formula. Term An individual number or element in an ordered list, identified by its position within the sequence. Index A positive integer indicating the position of a term within an ordered list, typically represented by n. Finite Sequence An ordered list of numbers with a definite end, containing a specific number of terms. Infinite Sequence An ordered list of numbers that continues indefinitely without a final term, often denoted with ellipsis. Explicit Formula An equation involving n that allows direct calculation of any term in an ordered list without reference to previous terms. Recursive Formula A rule that defines each term in an ordered list based on one or more preceding terms, requiring initial values. Arithmetic Sequence An ordered list where each term increases or decreases by a constant value, forming a linear pattern. Exponential Sequence An ordered list where each term is a constant raised to the power of the index, resulting in rapid growth or decay. Fractional Sequence An ordered list where terms are fractions, often with numerators and denominators following distinct patterns. Pattern A recognizable regularity or rule that determines the progression of terms in an ordered list. Subscript Notation A way to label terms in an ordered list using a variable with a subscript, such as aₙ, to indicate position. Alternating Sequence An ordered list where the sign or value of terms alternates in a regular fashion, often involving powers of negative one. General Formula A mathematical expression that provides a direct method to compute any term in an ordered list based on its position. Function A mathematical relationship similar to an ordered list, but with inputs that can be any real number, not just positive integers.
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