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Mastering Patterns in Sequences

Understand and identify arithmetic and geometric sequences by recognizing and extending patterns. Practice determining terms in sequences using addition and multiplication methods.

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Mastering Patterns in Sequences

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  1. Transparency 7 Click the mouse button or press the Space Bar to display the answers.

  2. Splash Screen

  3. Example 7-4b Objective Recognize and extend patterns for sequences

  4. Example 7-4b Vocabulary Sequence An ordered list of numbers

  5. Example 7-4b Vocabulary Term Each number in a sequence 8, 11, 14, 17, 20 . . .

  6. Example 7-4b Vocabulary Arithmetic sequence Each term is found by adding the same number to the previous term 8, 11, 14, 17, 20 . . . 3 is added to each term to get the next term

  7. Example 7-4b Vocabulary Geometric sequence Each term is found by multiplying the previous term by the same number 3, 6, 12, 24, 48 . . . 2 is multiplied to each term to get the next term

  8. Lesson 7 Contents Example 1Describe Patterns in Sequences Example 2Describe Patterns in Sequences Example 3Determine Terms in Sequences Example 4Determine Terms in Sequences

  9. Example 7-1a Describe the pattern in the sequence and identify the sequence as arithmetic, geometric, or neither. 3, 6, 12, 24, … Write problem 3, 6, 12, 24, … Determine how the series goes from the 3 to the 6 Remember: Sometimes there is more than one way Add 3 or Multiply by 2 Which pattern will get the 6 to 12? 1/4

  10. Example 7-1a Describe the pattern in the sequence and identify the sequence as arithmetic, geometric, or neither. 3, 6, 12, 24, … Add 3 or Multiply by 2 3, 6, 12, 24, … Which pattern will get the 6 to 12?    Does multiplying by 2 get the 12 to the 24? The pattern is multiplying by 2 The pattern is multiplying by 2 1/4

  11. Example 7-1a Describe the pattern in the sequence and identify the sequence as arithmetic, geometric, or neither. 3, 6, 12, 24, … Add 3 or Multiply by 2 3, 6, 12, 24, …    Name the sequence Remember: Arithmetic is adding the same number Geometric is multiplying the same number Geometric Multiply by 2 Answer:Multiplying by 2 ; geometric 1/4

  12. Example 7-1b Describe the pattern in the sequence and identify the sequence as arithmetic, geometric, or neither. 5, 9, 18, 22, 31, … Answer: Add 4, add 9; neither. 1/4

  13. Example 7-2a Describe the pattern in the sequence and identify the sequence as arithmetic, geometric, or neither. 7, 11, 15, 19, … Write problem Determine how the series goes from the 7 to the 11 7, 11, 15, 19, … Remember: Sometimes there is more than one way Add 4 Determine how the series goes from the 11 to the 15 Add 4 2/4

  14. Example 7-2a Describe the pattern in the sequence and identify the sequence as arithmetic, geometric, or neither. 7, 11, 15, 19, … Determine how the series goes from the 15 to the 19 7, 11, 15, 19, … Add 4 The pattern is adding 4 Arithmetic Now identify the pattern Pattern is adding the same number each time Answer: Add 4; Arithmetic sequence 2/4

  15. Example 7-2b Describe the pattern in the sequence and identify the sequence as arithmetic, geometric, or neither. 3, 11, 19, 27, … Answer: Add 8; arithmetic. 2/4

  16. Example 7-3a Write the next three terms of the sequence. 5, 14, 23, 32, ... Write problem 5, 14, 23, 32, … Determine how the series goes from the 5 to 14 Remember: Sometimes there is more than one way Add 9 Determine how the series goes from the 14 to 23 Add 9 3/4

  17. Example 7-3a Write the next three terms of the sequence. 5, 14, 23, 32, ... Determine how the series goes from the 23 to 32 5, 14, 23, 32, … Add 9 Use the pattern of adding 9 to determine the next three terms Add 9 to 32 Add 9 to 41 Add 9 to 50 Answer: 41, 50, and 59. 3/4

  18. Example 7-3b Write the next three terms of the sequence. 12, 17, 22, 27, … Answer: 32, 37, 42 3/4

  19. Example 7-4a Write the next three terms of the sequence. 0.2, 1.2, 7.2, 43.2, … Write problem Determine how the series goes from the 0.2 to 1.2 0.2, 1.2, 7.2, 43.2, Remember: Sometimes there is more than one way 6 6 Add 1 and multiply 6 Determine how the series goes from the 1.2 to 7.2 Adding 1 does not work Multiply by 6 does work 4/4

  20. 9,331.2 Example 7-4a Write the next three terms of the sequence. 0.2, 1.2, 7.2, 43.2, … Determine how the series goes from the 7.2 to 43.2 0.2, 1.2, 7.2, 43.2, Multiply by 6 6 6 6 Use the pattern of multiplying by 6 to determine the next three terms Multiply 43.2 by 6 Multiply 259.2 by 6 Multiply 1,555.2 by 6 Answer: 259.2, 1,555.2, and 9,331.2 4/4

  21. Example 7-4b * Write the next three terms of the sequence. 3, 12, 48, 192, … Answer: 768, 3,072, 12,288 4/4

  22. End of Lesson 7 Assignment

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