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Monday August 12, 2013

Monday August 12, 2013. Compare and contrast arithmetic and geometric sequences. Standard. MM4A9. Students will use sequences and series.

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Monday August 12, 2013

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  1. MondayAugust 12, 2013 Compare and contrast arithmetic and geometric sequences

  2. Standard • MM4A9. Students will use sequences and series. • c. Find and apply the sums of finite and, where appropriate, infinite arithmetic and geometric series.d. Use summation notation to explore finite series.

  3. Essential Questions • What’s the difference between infinite and finite sequences? • Why is it important to find the sum of a sequence?

  4. Immortality • In terms of life • Infinite, in terms of mathematics.

  5. Vocabulary • Series – the sum of the terms of a sequence. • Infinite sequence – a series consisting of an infinite number of terms. • Finite sequence – a series consisting of a finite, or limited, number of terms.

  6. Explicit Formula -a formula that allows direct computation of any term for a sequence. • Arithmetic • an = a1 + d(n-1) • Geometric • gn = g1 * r(n-1)

  7. Recursive Formula -a formula that allows direct computation of the succeeding term. • Arithmetic • an = an-1 + d • Geometric • gn = gn-1 * r

  8. Write an explicit formula for the sequence below

  9. Write an explicit formula for the sequence below

  10. Try # 11

  11. Try # 11 • an = -9n + 42

  12. Write a recursive formula for the sequence below

  13. Write a recursive formula for the sequence below

  14. Write a recursive formula for the sequence below

  15. Try # 21

  16. Try # 21

  17. What is a series?Calculate the sum for the following

  18. What is a series?Calculate the sum for the following

  19. What is a series?Calculate the sum for the following

  20. Try # 47

  21. Try # 47

  22. Worksheet 8-12-13

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