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Sequence Warm-Up: Arithmetic and Geometric Sequences

Practice solving arithmetic and geometric sequence problems, finding common differences and ratios, and writing explicit formulas.

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Sequence Warm-Up: Arithmetic and Geometric Sequences

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  1. Warm-up 1. Find 3f(x) + 2g(x) 2. Find g(x) – f(x) 3. Find g(-2)

  2. Go over Quiz

  3. Arithmetic Sequence A sequence of terms that have a common difference between them

  4. Geometric Sequence A sequence of terms that have a common ratio between them

  5. Explicit Formula Formula used to find the nth term of a sequence

  6. Explicit Formula for Arithmetic Sequence

  7. Explicit Formula for Geometric Sequence

  8. Arithmetic or Geometric? Example: -22, -15, -8, -1, … Arithmetic d = 7

  9. Arithmetic or Geometric? Example: 7, 4, 1, -2, -5 Arithmetic d = -3

  10. Arithmetic or Geometric? Example: 256, 64, 16, 4, … Geometric r = 1/4

  11. Arithmetic or Geometric? Example: Geometric r = 2/3

  12. Find the common difference, the explicit formula, and the tenth term. 3, 9, 15, 21, … d = 6 an = 6n – 3 a10 = 57

  13. Find the common ratio, the explicit formula, and the seventh term. 3, 1.5, 0.75, 0.375, …

  14. The fifth term is 1,792. The constant ratio is 4. Write the explicit formula.

  15. Homework Sequence Practice WS

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