Algebra 2, Unit 6: Sequences and Series. 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 specific pattern
- What is a term in a sequence?
- Each individual number in the sequence
- What is an arithmetic sequence?
- A sequence with a constant difference between consecutive terms
- What is the common difference in an arithmetic sequence?
- The constant amount added to get the next term
- What is the explicit formula for an arithmetic sequence?
- a_n = a_1 + (n - 1)d
- What is a geometric sequence?
- A sequence with a constant ratio between consecutive terms
- What is the common ratio in a geometric sequence?
- The constant factor multiplied to get the next term
- What is the explicit formula for a geometric sequence?
- a_n = a_1 times r^(n - 1)
- What is a recursive formula for a sequence?
- A formula defining each term based on the previous term(s)
- What is a series?
- The sum of the terms of a sequence
- What is an arithmetic series?
- The sum of the terms of an arithmetic sequence
- What is the formula for the sum of a finite arithmetic series?
- S_n = n/2 times (a_1 + a_n)
- What is a geometric series?
- The sum of the terms of a geometric sequence
- What is the formula for the sum of a finite geometric series?
- S_n = a_1 times (1 - r^n) / (1 - r), for r not equal to 1
- What is an infinite geometric series?
- A geometric series with infinitely many terms
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