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?
- An ordered list of numbers following a pattern
- What is the general term (nth term) of a sequence often denoted as?
- a_n
- What is an arithmetic sequence?
- A sequence with a constant difference between terms
- What is a geometric sequence?
- A sequence with a constant ratio between terms
- What is a series?
- The sum of the terms of a sequence
- What is sigma notation used for?
- Compactly representing the sum of a sequence of terms
- What is the formula for the sum of a finite arithmetic series?
- S_n = n/2 times (a_1 + a_n)
- What is the formula for the sum of a finite geometric series?
- S_n = a_1(1 - r^n)/(1 - r)
- What is the formula for the sum of an infinite geometric series, if it converges?
- S = a_1 / (1 - r)
- Under what condition does an infinite geometric series converge?
- When the absolute value of the common ratio is less than 1
- What is a limit, in the context of sequences?
- The value a sequence's terms approach as n approaches infinity
- What does it mean for a sequence to converge?
- Its terms approach a specific finite value
- What does it mean for a sequence to diverge?
- Its terms do not approach any finite value
- What is the limit of a constant sequence?
- The constant value itself
- What is the limit as n approaches infinity of 1/n?
- 0
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