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Lesson 3.11 Concept : Arithmetic Sequences EQ : How do we recognize and represent arithmetic sequences? F.BF.1-2 & F.LE.2 Vocabulary: Arithmetic Sequences, recursive formula, explicit formula, common difference 1 3.10: Arithmetic Sequences

Lesson 3.11 Concept : Arithmetic Sequences

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Lesson 3.11 Concept : Arithmetic Sequences EQ : How do we recognize and represent arithmetic sequences? F.BF.1-2 & F.LE.2 Vocabulary: Arithmetic Sequences, recursive formula, explicit formula, common difference. Nature by Numbers. http:// www.youtube.com/watch?v=kkGeOWYOFoA. Introduction - PowerPoint PPT Presentation

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Lesson 3.11Concept: Arithmetic Sequences

EQ: How do we recognize and represent arithmetic sequences? F.BF.1-2 & F.LE.2

Vocabulary: Arithmetic Sequences, recursive formula, explicit formula, common difference13.10: Arithmetic Sequences23.10: Arithmetic Sequenceshttp://www.youtube.com/watch?v=kkGeOWYOFoA Nature by NumbersIntroductionAn arithmetic sequence is a list of terms separated by a common difference, d, which is the number added to each consecutive term in an arithmetic sequence.An arithmetic sequence is a linear function with a domain of whole numbers.

33.10: Arithmetic Sequences

Introduction (continued)Arithmetic sequences can be represented by formulas, either explicit or recursive.

A recursive formula is a formula used to find the next term of a sequence when the previous term is known.An explicit formula is a formula used to find the nth term of a sequence.

43.10: Arithmetic Sequences

453.10: Arithmetic SequencesCurrent TermPrevious TermCommon DifferenceFirst Term63.10: Arithmetic Sequences73.10: Arithmetic Sequences83.10: Arithmetic Sequences93.10: Arithmetic SequencesGuided PracticeExample 3Create the recursive formula that defines the sequence: An arithmetic sequence is defined by 10, 6, 2, 2, 1. Find the common difference, d.

103.10: Arithmetic Sequences113.10: Arithmetic Sequences123.8.1: Arithmetic SequencesGuided PracticeExample 4An arithmetic sequence is defined recursively by an = an 1 + 5, with a1 = 29. Find the first 5 terms of the sequence.Using the recursive formula: a1 = 29a2 = a1 + 5a2 = 29 + 5 = 34a3 = 34 + 5 = 39a4 = 39 + 5 = 44a5 = 44 + 5 = 49The first five terms of the sequence are 29, 34, 39, 44, and 49.

133.10: Arithmetic SequencesGuided PracticeExample 5An arithmetic sequence is defined recursively by an = an 1 8, with a1 = 68. Find the first 5 terms of the sequence.

The first five terms of the sequence are:____, ____, ____, ____, and ____

143.10: Arithmetic Sequences153.10: Arithmetic Sequences163.10: Arithmetic Sequences173.10: Arithmetic Sequences183.10: Arithmetic Sequences193.10: Arithmetic Sequences203.10: Arithmetic Sequences213.10: Arithmetic Sequences223.10: Arithmetic Sequences