1. Warm-Up #34 Thursday, 12/10

2. Homework Thursday, 12/10 Lesson 4.02 packet Pg____________________

3. Warm-Up #35 Friday, 12/11

4. Homework, Friday 12/11 Lesson 4.03 packet Pg 2 and

5. Lesson 4.02_Explicit and Recursive Form

7. Arithmetic Sequence It is a sequence that goes from one term to the next term by always adding or subtracting to the same value Example:

8. Common difference (notation= d) It is the difference between each number in an arithmetic sequence

9. Geometric Sequence It is a sequence that goes from one term to the next by always multiplying or dividing by the same value Example:

10. Common ratio (notation = r) It is the ratio of a term to the previous term in a geometric sequence.

11. Sequence A sequence always start with the 1 st term. Example: {3, 5, 7, 9…} So what is the 0 th term for this example? Explain. 1 st term 2 nd term

12. Practice Problems 1){24, 27, 30, …} 2)(56, 66, 76, …} 3){4, 16, 64…} 4){50, 25, 12.5, …}

13. Arithmetic Sequence If the sequence is an arithmetic sequence, then it is a linear function with an equation of y = mx + b

14. Geometric Sequence

15. 5-Minute Check 1 A.arithmetic B.geometric C.neither Which best describes the sequence 1, 4, 9, 16, …?

16. 5-Minute Check 2 A.arithmetic B.geometric C.neither Which best describes the sequence 3, 7, 11, 15, …?

17. 5-Minute Check 3 A.arithmetic B.geometric C.neither Which best describes the sequence 1, –2, 4, –8, …?

18. 5-Minute Check 4 A.–50, 250, –1250 B.–20, 100, –40 C.–250, 1250, –6250 D.–250, 500, –1000 Find the next three terms in the geometric sequence 2, –10, 50, ….

19. known values Explicit Formulas

20. What is a recursive sequence? Definition: A recursive sequence is the process in which each step of a pattern is dependent on the step or steps before it.

21. Recursion Formulas “Rate of change”

22. Sequence and Terms Let’s look at the following sequence 1,4,9,16,25,36,49,…, The letter a with a subscript is used to represent function values of a sequence. The subscripts identify the location of a term. Do you know what the rule is for the sequence? n²

23. How to read the subscripts: a term in the sequence the prior term the next term

24. Ex. 1: Find the first four terms of the sequence: The first term is 5 Each term after the first + 2 is 3 times the previous term Plus 2 Let’s be sure we understand what is given General Term

25. Continued… Ex. 1: Find the first four terms of the sequence: n=1 n=3 n=2 n=4 given Start with general term for n>1 Answer = 5, 17, 53, 161

26. Your turn: Ex 2: Find the next four terms of the sequence. given Start with general term for n>1 Answer = 3, 6, 12, 24 n=1 n=3 n=2 n=4

27. Try another… n=1 n=3 n=2 n=4 given = = 4 – 4 = 0 0 – 2 = -2 Answer = 2, 1, 0, -2, -8 n=5 = -8 – 0 = -8 given

28. Your turn Write a recursive formula for the sequences below. Step 1 : Determine if it is arithmetic or geometric. Step 2 : Plug in to either the geometric or arithmetic recursive formula. Step 3 : Make sure you tell us what a 1 is equal to. Ex. 3 7, 3, -1, -5, -9, … The common difference = -4 The first term = 7 Ex. 4 3, 6, 12, 24, 48, … The common ratio = 2 The first term = 3

29. The first row of the theater has 15 seats in it. Each subsequent row has 3 more seats that the previous row. If the last row has 78 seats, how many rows are in the theater? Example

30. https://www.youtube.com/watch?v=JkZIdi1A_TM https://www.youtube.com/watch?v=-XVIMMjtAmI https://www.youtube.com/watch?v=cpg82-TotYE