Sequences definitions Flashcards
Sequences definitions
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Sequence An ordered list of numbers, either finite or infinite, where each number is called a term and follows a specific pattern. Term An individual number in a sequence, identified by its position and often generated by a formula or pattern. Index A positive integer representing the position of a term within a sequence, typically denoted by n. Finite Sequence A sequence with a limited number of terms, ending at a specific value without continuing indefinitely. Infinite Sequence A sequence that continues without end, often indicated by an ellipsis after the last visible term. Pattern A recognizable regularity or rule that determines how terms in a sequence are generated or related. General Formula An explicit equation involving the index n, used to calculate any term in a sequence directly. Recursive Formula An equation that defines each term of a sequence based on one or more previous terms, requiring initial values. Arithmetic Sequence A sequence where each term increases or decreases by a constant difference from the previous term. Explicit Formula A synonym for general formula, providing a direct calculation for any term using the index. Subscript Notation A way to label terms in a sequence, such as a₁, a₂, a₃, indicating their position using subscripts. Fraction Sequence A sequence where terms are fractions, often with numerators and denominators following their own patterns. Exponential Sequence A sequence where each term is generated by raising a base number to the power of the index or a related expression. Alternating Sequence A sequence in which the sign or value of terms alternates, often modeled using powers of negative one. Function A mathematical relationship similar to a sequence, but with inputs that can be any real number, not just positive integers.
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