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P O D. basic. advanced. 12m + 12 + 3m − (-6). 5(3v + 2) + 2(-2v + 6v). 15v + 10 + (-4v) + 12v. 12m + 12 + 3m + 6. 15v + (-4v) + 12v + 10. 12m + 3m + 12 + 6. 11v + 12v + 10. 15m + 12 + 6. 23v + 10. 15m + 18. Sequences.

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  1. POD basic advanced 12m + 12 + 3m − (-6) 5(3v + 2) + 2(-2v + 6v) 15v + 10 + (-4v) + 12v 12m + 12 + 3m + 6 15v + (-4v) + 12v + 10 12m + 3m + 12 + 6 11v + 12v + 10 15m + 12 + 6 23v + 10 15m + 18

  2. Sequences A sequence is an ordered list of numbers. Each number in a sequence is called a term. In an arithmetic sequence, each term is found by adding the same number to the previous term.

  3. Example: Describe the relationship between the terms in the arithmetic sequence 8, 13, 18, 23, … . Then write the next three termsin the sequence. 5 is added to the previous term. The next three terms are 28, 33, and 38.

  4. In a sequence, each term has a specific position within the sequence. Consider the sequence 2, 4, 6, 8, … 3rd position 1st position 2, 4, 6, 8 2nd position 4th position Notice that as the position number increases by 1, the value of the term increases by 2.

  5. 3rd position 1st position 2, 4, 6, 8 2nd position 4th position You can write an algebraic expression to represent the relationship between any term and it’s position in the sequence. In this case, if n represents the position in the sequence, the value of the term is 2n.

  6. Whiteboard time Identify the relationship between the terms, then find the missing terms. 7, 14, 21, 28, ____ , ____ , … Add 7 to the previous term. The missing terms are 35, and 42

  7. Whiteboard time Identify the relationship between the terms, then find the missing terms. 1.5, 3, 4.5, ____ , 7.5, … Add 1.5 to the previous term. The missing term is 6

  8. Whiteboard time Identify the relationship between the terms, then find the missing terms. 0.3, ____ , 0.9, 1.2, 1.5, … Add 0.3 to the previous term. The missing term is 0.6

  9. Whiteboard time Identify the relationship between the terms, then find the missing terms. 21, 31.5, 42, ____ , 63, 73.5 … Add 10.5 to the previous term. The missing term is 52.5

  10. Which algebraic expression can be used to find the distance walked on any day? 3 + x 3x 4x x − 3 3x

  11. Which algebraic expression can be used to find out how much money can be earned in any number of hours? 7x 7.50x x + 7.50 x + 7 7.50x

  12. Write an algebraic expression that can be used to find the height of the sapling for any year. 12x

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