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Warm-Up: February 28, 2013 Find the next 3 terms:

Warm-Up: February 28, 2013 Find the next 3 terms:. 2, 4, 8, 16, … -54, -18, -6, … 3, -6, 12, -24, …. Homework Questions?. Geometric Sequences. Section 11.4. Essential Questions. How can we use geometric sequences to find any term? How can we calculate geometric means?. Definition.

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Warm-Up: February 28, 2013 Find the next 3 terms:

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  1. Warm-Up: February 28, 2013Find the next 3 terms: • 2, 4, 8, 16, … • -54, -18, -6, … • 3, -6, 12, -24, …

  2. Homework Questions?

  3. Geometric Sequences Section 11.4

  4. Essential Questions • How can we use geometric sequences to find any term? • How can we calculate geometric means?

  5. Definition • A geometric sequence is a sequence in which the ratio of successive terms is the same number, r, called the common ratio. • Multiply a term by r to get the next term.

  6. Example: Page 717 #9 • Determine whether each sequence is a geometric sequence. If so, identify the common ratio, r, and give the next three terms. • 20, 40, 80, 160, …

  7. You-Try: Page 717 #13 • Determine whether each sequence is a geometric sequence. If so, identify the common ratio, r, and give the next three terms. • 2, 10, 50, 250, …

  8. The Equation • tn is the nth term • t1 is the first term • n ≥ 1

  9. Better Equation • tn is the nth term • tm is the mth term • n, m are integers ≥1

  10. Finding a specific term • Find the common ratio, r. There could be two possible values: one positive, one negative. • Method 1 • Use the better formula and the values of r and tm to find tn • Method 2 • Multiply by r until you get to tn.

  11. Example: Page 718 #39 • Find the sixth term in the geometric sequence that includes each pair of terms. • t3 = 150, t5 = 3750

  12. You-Try: Page 718 #43 • Find the sixth term in the geometric sequence that includes each pair of terms. • t5 = 24, t8 = 3

  13. Geometric Means • Geometric means are the terms between two nonconsecutive terms of a geometric sequence. • Find the common ratio, r. There could be a positive and negative answer. • Multiply by r to get the missing terms. If there are two values of r, do this for both.

  14. Example: Page 718 #61 • Find three geometric means between -2 and -1/8.

  15. You-Try: Page 718 #63 • Find three geometric means between 486 and 6.

  16. Assignment • Page 717-718 #9-23 odd, 39-45 odd, 57-63 odd

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