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

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

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

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

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

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

Example 7-1a Describe the pattern in the sequence and identify the sequence as arithmetic, geometric, or neither. 3, 6, 12, 24, … 3, 6, 12, 24, … Write problem 1/4 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?

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

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

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

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

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

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

Example 7-3a Write the next three terms of the sequence. 5, 14, 23, 32,... 5, 14, 23, 32, … 3/4 Write problem 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

Example 7-3a Write the next three terms of the sequence. 5, 14, 23, 32,... 5, 14, 23, 32, … 3/4 Determine how the series goes from the 23 to 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.

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

Example 7-4a Write the next three terms of the sequence. 0.2, 1.2, 7.2, 43.2, … 0.2, 1.2, 7.2, 43.2, 4/4 66 Write problem Determine how the series goes from the 0.2 to 1.2 Remember: Sometimes there is more than one way 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 66

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

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

End of Lesson 7 Assignment Lesson 1:7Sequences All