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Exploring Linear Equations and Sequence Patterns

Delve into arithmetic sequences, function notation, and graphing patterns while understanding linear equations and modeling simpler sequences in this informative lesson. Practice calculating terms, identifying patterns, and solving problems involving shoe design and giraffes.

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Exploring Linear Equations and Sequence Patterns

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  1. Let’s Review Commutative Property Classify Numbers Multi-Step Equations Absolute Value Proportions/Percent of increase/decrease Inequalities : When to switch sign? Graphing Points Functions B.A.G.

  2. Unit 4 Lesson 5

  3. “I can…” • …determine if a sequence or pattern could be modeled by a linear equation and can model that pattern • M(F&A)-10-1

  4. RECALL: Function • A relation for which each input has exactly one output • Vertical Line Test

  5. RECALL: Function Notation

  6. SEQUENCE • A sequence is an ordered list of numbers that forms a pattern • Each number in the list is called a term of the sequence • Ex. • 5, 8, 11, 14,… • 2.5, 5, 10, 20, 40,…

  7. Determine if it is an Arithmetic sequence • Arithmetic-the difference between consecutive terms is constant, and is known as a common difference • Ex. Yes or No • 3, 8, 13, 18… • 10,4,-2,-8,… • 5,7,10,14,19,25,… • 2, -2, 2, -2, 2, -2,… • FORMULA

  8. Explicit Formula for an Arithmetic Sequence • Example • 10,4,-2,-8,…

  9. More Examples • 99,88,77,66,… • 23,38,53,68,… • Take the above two formulas and find the 12th term • Graph the Results

  10. Look for the patterns… • Term 1 • Term 2 • Term 3 • Term 4 • Term 5

  11. NECAP Prep Question

  12. Shoes! I want some shoes too! • You are designing shoes for giraffes, with 72 pairs of eyelets, how many cm’s long will the shoelaces be?

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