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Understanding and Extending Sequences: Patterns and Relationships

This lesson focuses on describing and extending various number sequences by identifying the relationships between their terms. Students will learn to recognize patterns, whether by addition, subtraction, multiplication, or division. Examples include sequences like 21, 19, 17, 15, and more complex sequences involving multiplication by 3 or division by 2. By the end of the lesson, students will be able to find the next terms in given sequences and understand the rules governing them, equipping them with skills for more advanced mathematical concepts.

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Understanding and Extending Sequences: Patterns and Relationships

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  1. Continue with More Sequences Splash Screen

  2. -2 -2 -2 More Sequences Describe and Extend Sequences Describe the relationship between the terms in the sequence 21, 19, 17, 15 … Then write the next three terms in the sequence. 21, 19, 17, 15 Each term is found by subtracting 2 from the previous term. Continue the pattern to find the next three terms. 15 - 2 = 13 13 - 2 = 11 11 - 2 = 9 Answer: The next three terms are 13, 11, and 9. Example 1

  3. A B C D More Sequences Describe the relationship between the terms in the sequence 34, 31, 28, 25… Then write the next three terms in the sequence. A. add 3; 28, 31, 34 B. subtract 3; 22, 19, 16 C. subtract 4; 21, 17, 13 D. Subtract 2; 23, 21, 19 Example 1

  4. •3 •3 •3 More Sequences Describe and Extend Sequences Describe the relationship between the terms in the sequence 2, 6, 18, 54… Then write the next three terms in the sequence. 2, 6, 18, 54 Each term is found by multiplying 3 to the previous term. Continue the pattern to find the next three terms. 54 • 3 = 162 162 • 3 = 486 486 • 3 = 1458 Answer: The next three terms are 162, 486, and 1458. Example 1

  5. ÷3 ÷3 ÷3 More Sequences Describe and Extend Sequences Describe the relationship between the terms in the sequence 2, 6, 18, 54… Then write the next three terms in the sequence. 729, 243, 81, 27 Each term is found by dividing 3 to the previous term. Continue the pattern to find the next three terms. 27 ÷ 3 = 9 9 ÷ 3 = 3 3 ÷ 3 = 1 Answer: The next three terms are 9, 3, and 1. Example 1

  6. A B C D More Sequences Describe the relationship between the terms in the sequence 2,048, 512, 128, 32, … Then write the next three terms in the sequence. A. Divide by 2; 16, 8, 4 B. Subtract 4; 28, 24, 20 C. Divide by 8; 4, 0.5, 0.0625 D. Divide by 4; 8, 2, 0.5 Example 2

  7. A B C D More Sequences Describe the relationship between the terms in the sequence 2, 8, 32, 128, … Then write the next three terms in the sequence. A. Add 96; 288, 384, 480 B. Multiply by 4; 512, 2,048, 8,192 C. Multiply by 2; 256, 512, 1,024 D. Add 6; 134, 140, 146 Example 2

  8. End of the Lesson End of the Lesson

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