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**Patterns and Sequences**

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

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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, ___ 7 5 9 10 25

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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? 6 2 1 4 3 5

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**Learn to find patterns and to recognize, describe, and extend patterns in sequences.**

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Vocabulary perfect square term arithmetic sequence

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**Each month, Eva chooses 3 new DVDs from her DVD club. Eva’s DVDs Month **

1 3 2 4 Position Value + 3 6 + 3 9 + 3 12 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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**A sequence is an ordered set of numbers**

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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**Look for a relationship between the 1st term and the 2nd term**

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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**Additional Example 1A: Extending Arithmetic Sequences**

Identify a pattern in each sequence and then find the missing terms. 48, 42, 36, 30, , , , . . . –6 –6 –6 –6 –6 –6 Look for a pattern. A pattern is to subtract 6 from each term to get the next term. 30 – 6 = – 6 = – 6 = 12 So 24, 18, and 12 will be the next three terms.

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**Additional Example 1B: Extending Arithmetic Sequences**

Position 1 2 3 4 5 6 Value of Term 9 22 35 48 +13 +13 +13 +13 +13 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.

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

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**1 2 3 4 5 6 7 16 25 34 Check It Out: Example 1B Position Value of Term**

+9 +9 +9 +9 +9 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.

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**Additional Example 2A: Completing Other Sequences**

Identify a pattern in the sequence. Name the missing terms. 24, 34, 31, 41, 38, 48, , , ,… +10 – – – –3 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.

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**Additional Example 2B: Completing Other Sequences**

Position 1 2 3 4 5 6 7 8 Value of Term 16 32 4 ÷2 A pattern is to multiply one term by 4 and divide the next by 2. 8 ÷ 2 = 4 4 4 = ÷ 2 = 4 = 32 So 4 and 8 will be the missing terms in the sequence.

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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. 30 2 = = 62 So 60 and 62 are the missing terms.

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**A pattern is to multiply one term by 6 and divide the next by 2.**

Check It Out: Example 2B Position 1 2 3 4 5 6 7 8 Value of Term 18 54 162 6 ÷2 6 ÷2 6 ÷2 6 A pattern is to multiply one term by 6 and divide the next by 2. 18 ÷ 2 = 9 9 6 = ÷ 2 = 6 = 162 So 9 and 27 will be the missing terms in the sequence.

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Lesson Quiz Identify a pattern in each sequence, and then find the missing terms. 1. 12, 24, 36, 48, , , , … 2. 75, 71, 67, 63, , , ,… Identify a pattern in each sequence. Name the missing terms. , 500, , 125,… 4. 100, 50, 200, , 400, ,… add 12; 60, 72, 84 subtract 4; 59, 55, 51 divide by 2; 250 divide by 2 then multiply by 4; 100, 200

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