Unit 10 Day 1 Geometric Sequences. Welcome! Please pick up a packet. Welcome! agenda. 07 MIN Warm Up 25 MIN Lesson 10.1 Notes 15 MIN Assignment

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1 Welcome! Please pick up a packet. Welcome! agenda 07 MIN Warm Up 25 MIN Lesson 10.1 Notes 15 MIN Assignment

2 Plus unıt 10: exponentıal functıons Learning Targets I can define orally and in writing: sequence, term (u 1 ), general term (u n ), recursive formula, recursive rule, arithmetic sequence, common difference, geometric sequence, common ratio I can write the recursive formula for an arithmetic and geometric sequence. I can read and write recursive formulas with subscript notation. I can find terms of a sequence given recursively.

3 warm up [1] Two angles are supplementary and have a ratio of 1:4. What is the measure of the smaller angle? a. 36 b. 18 c. 72 d. 45 e. 144 A [2] One-half of the measure of the supplement of angle ABC is equal to twice the measure of angle ABC. What is the measure, in degrees, of the complement of angle ABC? a. 90 b. 18 c. 36 d. 72 e. 54 E Recall from Semester 1... Vocabulary: Defn of Sequence: an ordered list of numbers Each number in a sequence is called a.

4 Arithmetic Sequence: is a sequence where each term is just the previous term plus a constant. The constant is called the Common Difference How to identify an arithmetic sequence... Are these arithmetic? If so, what is the common difference? ex) 2, 5, 8, 11,... ex) 10, 4, 1, 3,... ex) 91.4, 83.1, 74.8, 66.5, Geometric Sequence: a sequence where each term is just the previous term multiplied by a constant. The constant is called the common ratio or the common multiplier How to identify a geometric sequence... Are these geometric? If so, what is the common ratio? ex) 5, 10, 20, 40,... ex) 30, 10, 3.3, 1.1,... ex) 64.2, , , ex) 1, 1, 2, 3, 5, 8,...

5 These sequences are all RECURSIVE. Recursion: where each step of a pattern is dependent on the step or steps before it. Recursive Formula Creates a sequence. It contains the following pieces: Starting value: The first number in the series. u 0 or u 1 Recursive rule: defines the n th term in relation to the previous term (or terms) Condition: tells which values of n the rule will work for. Write a recursive routine to represent each type of sequence. Arithmetic Sequence Geometric Sequence

6 Let's come up with a recursive formula to show the following pattern and find the next 3 terms. ex) 5, 20, 80,,, Arithmetic or Geometric? Recursive Routine ex) 30, 10, 3.3, 1.1,... Recursive Routine Is there a way to do this on my calculator?

7 ex) 5, 20, 80,,, Recursive Routine u 1 = 5 u n = u n 1 x 4 On your home screen type the following 5 enter ans x 4 enter, enter, enter... You MUST count how many iterations you have done. Use this to find the 15th term! What if I don't want to count or loose track while counting?

8 ex) 5, 20, 80,,, Recursive Routine u 1 = 5 u n = u n 1 x 4 Enter the starting term and value on your calculator like this: {1, 5} then press enter. Next, enter this: {Ans (1)+1, Ans (2) x 4} And keep hitting enter until you get to the term you need. OYO 24, 12, 6,... Arithmetic or Geometric? Recursive Routine: Find the 15th term:

9 OYO: Find the pattern for the number of black triangles! Arithmetic or Geometric? Recursive Routine: Find the number black triangles at stage 20. Find the missing terms: 1) Arithmetic: 5,,, 14,, 2) Geometric: 48,,, 6,,

10 ex) The amount of money Tony had in his lunch account before eating any lunches this year was $46. The amount remaining after the first day was $ The amount remaining after the second day was $41. a) Starting value b) Arithmetic or Geometric? Common Difference or Ratio: c) Recursive rule: d) Find u 10. What does this value mean? e) When will Tony's account run out of money? ex) Every month, I take a count of the number of rabbits in her vegetable patch. The first month, I counted 12. The second month, 18, and the third month 27. a) Starting value b) Arithmetic or geometric? Common Difference or Ratio: c) Recursive rule: d) Find u 8. What does this value mean?

11 Did you meet the goal? I can define orally and in writing: sequence, term (u1), general term (un), recursive formula, recursive rule, arithmetic sequence, common difference, geometric sequence, common ratio I can write the recursive formula for an arithmetic and geometric sequence. I can read and write recursive formulas with subscript notation. I can find terms of a sequence given recursively. Assignment: Geometric Sequences WS

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