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Bellwork

Bellwork. Extend each pattern 3 more terms, then describe in words how each term relates to the one previous. a) -3, 0, 3, 6, … b) 2, 4, 8, … c). 9, 12, 15. Each term is the previous term plus 3. 16, 32, 64. Each term is the previous term multiplied by 2.

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Bellwork

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  1. Bellwork • Extend each pattern 3 more terms, then describe in words how each term relates to the one previous. a) -3, 0, 3, 6, … b) 2, 4, 8, … c) 9, 12, 15 Each term is the previous term plus 3 16, 32, 64 Each term is the previous term multiplied by 2 Each term is the previous term multiplied by 1/2

  2. End in Mind • Title your notes page Sequences- Day 1 • Put a sub-header “End-in-mind” • Copy the problems below and use any strategies/resources to solve. A) A car whose original value was $25,000 decreases in value by $120 per month. How long will it take before the car’s value falls below $20,000? B) A car whose original value was $25,000 decreases in value by 5% per month. After 2 years, how much will the car be worth?

  3. Vocabulary • Sequences: A set of values arranged in a specific order, a pattern • Recursive Process: Used to describe a pattern or sequence by describing how to get from one term to the next. • Explicit Expression: Used to describe a pattern or sequence so that any term in the sequence can be found.

  4. (Vocabulary Continued) The value added each time is called the "common difference" The common difference could also be negative: Example: 25, 23, 21, 19, 17, 15, ... This common difference is −2 We call the common difference ‘d’

  5. (Vocabulary Continued) The value multiplied each time is called the "common ratio" The common ratio could also be a fraction: Example: 48, 24, 12, 6, 3, 1.5, ... This common ratio is 1/2 We call the common ratio ‘r’

  6. Use a Recursive Process to determine the 10th y-value Each y-value is the previousone plus 4. +4 So the 10th term is… 41 +4 +4 Arithmetic

  7. Use an Explicit Expression to find the 10th term Still Arithmetic Remember: We added 4 each time… Each y-value is the x-value times 4, plus 1. +1 +4 So… y=4x+1 +1 +4 +4 +1 +4 +4 +4 and the 10th term is… y = 4(10)+1 = 41 +1 +4 +4 +4 +4 x4, +1

  8. To determine the Explicit Expression for Arithmetic Sequences • Determine what you are adding each time. Added 4 each time, so we start off with y=4x… 2) Adjust to fit the pattern y=4x would lead to… y=4(1)=4 Our first term is -2, NOT 4. So we need to subtract 6. y=4x-6

  9. Sequences Day 1- I.C. Practice For each of the following arithmetic sequences. (a) Determine the 8th term using the Recursive process. (b) Determine the 20th term using an Explicit Expression. 1. 2. 3. I will come around and check these as you complete them.

  10. Notation: • d= common difference (what is added to each term of an arithmetic sequence) • r= common ratio (what is multiplied to each term of a geometric sequence) • n= What term number you are looking at (4th term, 10th term… nth term)

  11. Ticket Out • Come up with your own example of a sequence and state the explicit expression that corresponds with it. • What is something enjoyable you did over the weekend?

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