Arithmetic Sequences definitions Flashcards
Arithmetic Sequences definitions
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Arithmetic Sequence A list of numbers where the difference between consecutive terms remains constant throughout. Common Difference The fixed value added or subtracted between consecutive terms in an arithmetic sequence, often denoted as d. Recursive Formula An equation that defines each term of a sequence using the previous term and the common difference. General Formula An explicit equation that allows direct calculation of any term in a sequence using its position, the first term, and the common difference. First Term The initial value from which an arithmetic sequence begins, often denoted as a₁. Nth Term A specific term in a sequence identified by its position, calculated using the general formula. Index A number indicating the position of a term within a sequence, typically represented by n. Consecutive Terms Two terms that appear one after the other in a sequence. Positive Common Difference A situation where each term in the sequence increases by a fixed amount. Negative Common Difference A situation where each term in the sequence decreases by a fixed amount. Explicit Formula Another name for the general formula, providing a direct way to find any term without previous terms. Sequence An ordered list of numbers following a specific pattern or rule. Term An individual number or element within a sequence. Pattern A recognizable regularity or rule that defines the progression of terms in a sequence. Subscript Notation A way to label terms in a sequence using indices, such as a₁, a₂, a₃, etc.
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