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

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

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

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

Vocabulary perfect square term arithmetic sequence

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, …

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.

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

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 = 24 24 – 6 = 18 18 – 6 = 12 So 24, 18, and 12 will be the next three terms.

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. 48 + 13 = 61 61 + 13 = 74 So 61 and 74 will be the next terms in the arithmetic sequence.

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 = 19 19 – 5 = 14 14 – 5 = 9 So 19, 14, and 9 will be the next three terms.

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. 34 + 9 = 43 43 + 9 = 52 So 43 and 52 will be the next terms in the arithmetic sequence.

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

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 = 16 16 ÷ 2 = 8 8  4 = 32 So 4 and 8 will be the missing terms in the sequence.

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

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 = 54 54 ÷ 2 = 27 27  6 = 162 So 9 and 27 will be the missing terms in the sequence.

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. 3. 1000, 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