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Mathematics LibreTexts

Key Terms Chapter 12: Sequences, Series, and Binomial Theorems

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    Example and Directions
    Words (or words that have the same definition)The definition is case sensitive(Optional) Image to display with the definition [Not displayed in Glossary, only in pop-up on pages](Optional) Caption for Image(Optional) External or Internal Link(Optional) Source for Definition
    (Eg. "Genetic, Hereditary, DNA ...")(Eg. "Relating to genes or heredity")The infamous double helix; Delmar Larsen
    Glossary Entries
    annuityAn annuity is an investment that is a sequence of equal periodic deposits.    
    arithmetic sequenceAn arithmetic sequence is a sequence where the difference between consecutive terms is constant.    
    common differenceThe difference between consecutive terms in an arithmetic sequence, \(a_n−a_{n−1}\), is \(d\), the common difference, for \(n\) greater than or equal to two.    
    common ratioThe ratio between consecutive terms in a geometric sequence, \(\frac{a_n}{a_{n−1}}\), is \(r\), the common ratio, where \(n\) is greater than or equal to two.    
    finite sequenceA sequence with a domain that is limited to a finite number of counting numbers.    
    general term of a sequenceThe general term of the sequence is the formula for writing the \(n\)th term of the sequence. The \(n\)th term of the sequence, \(a_n\), is the term in the \(n\)th position where \(n\) is a value in the domain.    
    geometric sequenceA geometric sequence is a sequence where the ratio between consecutive terms is always the same    
    infinite geometric seriesAn infinite geometric series is an infinite sum infinite geometric sequence.    
    infinite sequenceA sequence whose domain is all counting numbers and there is an infinite number of counting numbers.    
    partial sumWhen we add a finite number of terms of a sequence, we call the sum a partial sum.    
    sequenceA sequence is a function whose domain is the counting numbers.    
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