Precalculus, Unit 7: Sequences, Series, and Limits. Key terms, formulas, and worked-example cues a high school student meets for this unit, building on prior units. Front: the term, formula name, or short problem cue. Back: the definition, formula, or solution method.
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- What is a sequence?
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An ordered list of numbers following a pattern- What is the general term (nth term) of a sequence often denoted as?
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a_n- What is an arithmetic sequence?
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A sequence with a constant difference between terms- What is a geometric sequence?
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A sequence with a constant ratio between terms- What is a series?
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The sum of the terms of a sequence- What is sigma notation used for?
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Compactly representing the sum of a sequence of terms- What is the formula for the sum of a finite arithmetic series?
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S_n = n/2 times (a_1 + a_n)- What is the formula for the sum of a finite geometric series?
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S_n = a_1(1 - r^n)/(1 - r)- What is the formula for the sum of an infinite geometric series, if it converges?
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S = a_1 / (1 - r)- Under what condition does an infinite geometric series converge?
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When the absolute value of the common ratio is less than 1- What is a limit, in the context of sequences?
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The value a sequence's terms approach as n approaches infinity- What does it mean for a sequence to converge?
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Its terms approach a specific finite value- What does it mean for a sequence to diverge?
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Its terms do not approach any finite value- What is the limit of a constant sequence?
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The constant value itself- What is the limit as n approaches infinity of 1/n?
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