Warm Up Problem of the Day Lesson Presentation Lesson Quizzes

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 sequence term arithmetic sequence

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

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.

Not all sequences are arithmetic sequences. In nonarithmetic sequences, look for patterns that involve multiplication or division. Some sequences may even be combinations or different operations.

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 to 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 Quizzes Standard Lesson Quiz Lesson Quiz for Student Response Systems

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 and multiply by 4; 100, 200

Lesson Quiz for Student Response Systems 1. Identify the missing terms in the sequence. 14, 28, 42, 56, __ , __ , __ , ... A. 70, 84, 98 B. 69, 82, 95 C. 68, 80, 92 D. 67, 78, 89

Lesson Quiz for Student Response Systems 2. Identify the missing terms in the sequence. 65, 62, 59, 56, __ , __ , __ , ... A. 51, 46, 41 B. 52, 48, 44 C. 53, 50, 47 D. 54, 52, 50

Lesson Quiz for Student Response Systems 3. Identify the missing term in the sequence. 2500, 500, __ , 20, ... A. 100 B. 90 C. 80 D. 70

Lesson Quiz for Student Response Systems 4. Identify the missing terms in the sequence. 300, 100, 600,__ , 1200, __ ... A. 200, 300 B. 200, 400 C. 300, 600 D. 300, 800