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Course Patterns and Sequences 1-7 Patterns and Sequences Course 1 Warm Up Warm Up Lesson Presentation Lesson Presentation Problem of the Day Problem of the Day

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Course Patterns and Sequences Warm Up Determine what could come next. 1. 3, 4, 5, 6, ___ 2. 10, 9, 8, 7, 6, ___ 3. 1, 3, 5, 7, ___ 4. 2, 4, 6, 8, ___ 5. 5, 10, 15, 20, ___

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Course Patterns and Sequences Problem of the Day How can you place the numbers 1 through 6 in the circles so that the sums along each side are equal?

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Course Patterns and Sequences Learn to find patterns and to recognize, describe, and extend patterns in sequences.

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Course Patterns and Sequences Vocabulary perfect square term arithmetic sequence

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Course Patterns and Sequences Each month, Eva chooses 3 new DVDs from her DVD club. Evas DVDs MonthDVDs Value Position The number of DVDs Eva has after each month shows a pattern: Add 3. This pattern can be written as a sequence. 3, 6, 9, 12, 15, 18, …

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Course Patterns and Sequences A sequence is an ordered set of numbers. Each number in the sequence is called a term. In this sequence, the first term is 3, the second term is 6, and the third term is 9. When the terms of a sequence change by the same amount each time, the sequence is an arithmetic sequence.

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Course Patterns and Sequences Look for a relationship between the 1st term and the 2nd term. Check if this relationship works between the 2nd term and the 3rd term, and so on. Helpful Hint

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Course Patterns and Sequences Additional Example 1A: Extending Arithmetic Sequences Identify a pattern in each sequence and then find the missing terms. 48, 42, 36, 30,,,,... Look for a pattern. A pattern is to subtract 6 from each term to get the next term. 30 – 6 = 2424 – 6 = 1818 – 6 = 12 So 24, 18, and 12 will be the next three terms. –6 –6 –6 –6 –6 –6

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Course Patterns and Sequences Additional Example 1B: Extending Arithmetic Sequences A pattern is to add 13 to each term to get the next term = = 74 So 61 and 74 will be the next terms in the arithmetic sequence. Position Value of Term

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Course Patterns and Sequences Check It Out: Example 1A Identify a pattern in each sequence and name the next three terms. 39, 34, 29, 24,,,,... Look for a pattern. A pattern is to subtract 5 from each term to get the next term. 24 – 5 = 1919 – 5 = 1414 – 5 = 9 So 19, 14, and 9 will be the next three terms. –5 –5 –5 –5 –5 –5

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Course Patterns and Sequences Check It Out: Example 1B A pattern is to add 9 to each term to get the next term = = 52 So 43 and 52 will be the next terms in the arithmetic sequence. Position Value of Term

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Course Patterns and Sequences Additional Example 2A: Completing Other Sequences Identify a pattern in the sequence. Name the missing terms. 24, 34, 31, 41, 38, 48,,,,… A pattern is to add 10 to one term and subtract 3 from the next. 48 – 3 = = – 3 = 52 So 45, 55, and 52 are the missing terms. +10 –3 +10 –3

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Course Patterns and Sequences Additional Example 2B: Completing Other Sequences A pattern is to multiply one term by 4 and divide the next by 2. 8 ÷ 2 = = ÷ 2 = = 32 So 4 and 8 will be the missing terms in the sequence. Position Value of Term ÷

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Course Patterns and Sequences Check It Out: Example 2A Identify a pattern in each sequence and name the missing terms. 6, 12, 14, 28, 30,,,... A pattern is to multiply one term by 2 and add 2 from the next = = 62 So 60 and 62 are the missing terms

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Course Patterns and Sequences Check It Out: Example 2B A pattern is to multiply one term by 6 and divide the next by ÷ 2 = = ÷ 2 = = 162 So 9 and 27 will be the missing terms in the sequence. 6 ÷2 6 6 Position Value of Term ÷2 6

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Course Patterns and Sequences Lesson Quiz Identify a pattern in each sequence, and then find the missing terms , 24, 36, 48,,,, … 2. 75, 71, 67, 63,,,,… Identify a pattern in each sequence. Name the missing terms , 500,, 125,… , 50, 200,, 400,,… subtract 4; 59, 55, 51 add 12; 60, 72, 84 divide by 2; 250 divide by 2 then multiply by 4; 100, 200

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