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Geometric and Arithmetic Sequences

Geometric and Arithmetic Sequences. Homework Answers #1-5. 1. Geometric common ratio=3 2. Arithmetic common difference=20 3. Neither 4. Arithmetic common difference=100 5. Geometric common ratio=3. Homework Answers #6-9. 6. 7, 14, 28, 56, 112, 224 7. 7, 9, 11, 13, 15, 17

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Geometric and Arithmetic Sequences

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  1. Geometric and Arithmetic Sequences

  2. Homework Answers #1-5 • 1. Geometric common ratio=3 • 2. Arithmetic common difference=20 • 3. Neither • 4. Arithmetic common difference=100 • 5. Geometric common ratio=3

  3. Homework Answers #6-9 • 6. 7, 14, 28, 56, 112, 224 • 7. 7, 9, 11, 13, 15, 17 • 8. 3, 15, 75, 375, 1875, 9375 • 9. 4, 19, 34, 49, 64, 79

  4. Answer #10-11 • 10. Exponentially because the numbers are increasing by multiplies of 2 • (common ratio=2) • 11. The initial value is different and the common ratio is different.

  5. From Geometric Sequences to Tables and graphs • The geometric sequence from the Brown Tree Snake problem (1,5,25,125,625…) can be written in the from of a table below.

  6. Toolkit (Write in notes)

  7. Answer for #1-4 • 1. The information tell you that in two years the lizard population is 40. • 2. The point tells you that in one year the lizard population is 20. • 3. The population will exceed 100 in about 3 and a half years. • 4. List the values that represent the y-values (the population of the lizards) for each year divide the successive number by the previous number to get the common ratio -r

  8. Answer #5-6 • 5. the initial term would be10. • 6. continue to multiply the terms in the sequence by the common ratio until you reach the 10th term.

  9. The Mice Problem # 1-3 • 1. There were 12 mice in the population at 0 months. • 2. 12, 36, 108, 324, 972….. • 3. The sequence is geometric because the population of rats are increasing by multiplies of 3. (not by adding or subtracting a common number)

  10. The Mice Problem #4-5

  11. Mice Problem # 5 • The graph of the table will be a curved line because the sequence is not arithmetic and the population numbers are growing very rapidly.

  12. Mice Problem # 6 (graph)

  13. Mice problem #6 a - b • A. The scale for x is counting by one’s • B. The scale for y is counting by 200’s

  14. Ladybug Invasion #1-4 • 1. 5, 15, 25, 35, 45….. • 2. the common difference is 10 • 3. • 4. It will take 20 months

  15. Ladybug Invasion #5-8 • 5. 5, 50, 500, 5000, 50000 • 6. r=10 • 7. • 8. I would take more than 1 year, but less than two years for the population to reach 200.

  16. Ladybug Invasion #8 Exponential Growth Linear Growth Population Population Months Months

  17. Ladybug Invasion

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