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Understanding Geometric Sequences: Analysis, Functions, and Formulas

This lesson covers the fundamentals of geometric sequences, focusing on identifying common ratios and calculating terms using both explicit and recursive formulas. Students will explore sequences through graphical representation and pairing terms with their position numbers. Homework exercises include determining the common ratio for various sequences and practicing the use of explicit and recursive formulas. Key concepts include recognizing geometric sequences, understanding geometric means, and applying formulas in different contexts.

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Understanding Geometric Sequences: Analysis, Functions, and Formulas

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  1. Warm Up 1 2 3 4 5 128 64 32 16 8 Graph the sequence 128, 64, 32, 16, 8 • Make a table pairing each term with its position number What function does your scatterplot look like? In fact, a ______________ sequence is a _______________ function. Domain: Range:

  2. GeometricSequences Unit 6 Notes (Part 1) AA1.CC

  3. What does geometric mean? • A geometric sequence is a list of numbers with a common ratio (r) • A common ratio means you are MULTIPLYING the same amount between each term

  4. Ex.1Determine if the sequence is geometric. If so, find the common ratio. 1) -2, 6, -18, 54, … 2) 2, 4, 6, 8, … 3) -1, -5, -25, -125, … HW: #1-6

  5. Geometric Explicit Formula Common ratio First Term Yep, you need to memorize this one too!

  6. Ex.2 Given the explicit formula for a geometric sequence, find the common ratio and the 2nd and 6thterm. Common ratio First Term -6 2nd term: 6th term: -96 HW: #7-10

  7. Ex.3 Given the explicit formula for a geometric sequence, find the common ratio and the first five terms. HW: #7-10

  8. Geometric Recursive Formula Previous Term Common ratio

  9. Ex.4 Given the recursive formula for a geometric sequence, find the common ratio and the first five terms. HW: #11-14 Common ratio

  10. PracticeFind r and first 5 terms Explicit Recursive Common ratio Common ratio 2, -8, 32, -128, 512 3, 12, 48, 192, 768

  11. Ex.5Find the common ratio, recursive formula, and the Explicit Formula Just like arithmetic recursive, you are relying on the previous answer. Find the pattern again (this will be your “r”) -2, 6, -18, 54, … HW: #11-14

  12. PracticeFind the common ratio, recursive formula, and the explicit formula. 1) 1, 2, 4, 8, ….. 2) -3, 12, -48, 192, … HW: #11-14

  13. Homework:(Part 1) Geometric sequence worksheet #1-14

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