 How can an expression or process be determined for an...

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Module 7 Note-Taking and Study Guide FLVS Algebra 2 V19 Sequences and Series Lesson 7.01 Arithmetic Sequences and Series How can an expression or process be determined for an arithmetic sequence? What functions combine to create an explicit formula for arithmetic sequences? What possible restrictions exist on domains and ranges of arithmetic sequences? How do arithmetic sequences and series differ? What important information must be included to find a sum of an arithmetic series? Key Concepts Practice Recursive sequence formula: 𝑎𝑎 𝑛𝑛 = 𝑎𝑎 𝑛𝑛−1 + 𝑑𝑑 Explicit sequence formula: 𝑎𝑎 𝑛𝑛 = 𝑎𝑎 1 + 𝑑𝑑 ( 𝑛𝑛 − 1) d = common difference Series formula: 𝑆𝑆 𝑛𝑛 = 𝑛𝑛 2 ( 𝑎𝑎 1 + 𝑎𝑎 𝑛𝑛 ) Alternative series formula: 𝑆𝑆 𝑛𝑛 = 𝑛𝑛 2 [2 ∗ 𝑎𝑎 1 + 𝑑𝑑 ( 𝑛𝑛 − 1)] Domain restricted to integers greater than 1 1. Identify the 37 th term of the arithmetic sequence 2, 7, 12,… 2. What is the sum of a 44-term arithmetic sequence where the first term is -9 and the last term is 120?

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