2. Sequences A sequence is an ordered list of numbers that often form a pattern. Each number in the list is called a term of the sequence. A wooden post-and-rail fence is made as shown below. How many pieces of wood are needed to build a 4-section fence, a five-section fence, a six-section fence? 1 section 4 pieces 2 sections 7 pieces 3 sections 10 pieces I think I see a pattern. + 3 4-section fence 13 pieces 5-section fence 16 pieces 6-section fence 19 pieces That was easy

3. Extending Sequences Describe a pattern in each sequence. Determine what the next two terms are. 5, 8, 11, 14,… + 3 17, 20 3, 6, 12, 24,… * 2 48, 96 400, 200, 100, 50,… * ½ 25, 12.5 2, -4, 8, -16,… * -2 32, -64 8, 3, -2, -7,… - 5 -12, -17 That was easy

4. Arithmetic Sequences In an arithmetic sequence the difference between consecutive terms is constant. This difference is called the common difference. 3, 8, 13, 18,… + 5 There is a common difference of 5, so it is arithmetic. 9, 2, -5, -12,… - 7 There is a common difference of -7, so it is arithmetic. 5, 9, 12, 14,… + 4 + 3 + 2 There is no common difference, so it is not arithmetic. That’s not a common difference. Asi De Facil An arithmetic sequence follows a pattern of adding a fixed amount from one term to the next. 2, 6, 18, 54,… *3 That’s not adding. There is no common difference derived by addition, so it is not arithmetic.

5. Identifying Arithmetic Sequences Tell whether the sequence is arithmetic. If it is, what is the common difference? 8, 15, 22, 30,… + 7 + 8 No 10, 4, -2, -8,… -6 Yes CD = -6 7, 9, 11, 13,… + 2 Yes CD = +2 2, -2, 2, -2,… * -1 No 0.2, 1.5, 2.8, 4.1,… + 1.3 Yes CD = + 1.3 2, 11, 21, 32,… + 9 + 10 + 11 No

6. Practice with Sequences a) Describe a pattern in each sequence. b) Determine what the next two terms are. c) Explain why the sequence is or is not arithmetic. 7, 3, -1, -5,…2, 4, 8, 16,… 1, -3, 9, -27,…12, 19, 26, 33,… - 4 a) Add negative 4 b) -9, -13 c) It is arithmetic because the common difference is 4 and the pattern is addition. * 2 a) Multiply by 2 b) 32, 64 c) It is not arithmetic because there is not a common difference derived by addition. * -3 a) Multiply by negative 3 b) 81, -243 c) It is not arithmetic because there is not a common difference derived by addition. +7 a) Add 7 b) 40, 47 c) It is arithmetic because the common difference is 7 and the pattern is addition.

7. Homework Page 279: 10 – 28 Even Numbers

8. Recursive Formula A recursive formula is a function rule that relates each term of a sequence after the first term to the ones before it. 3, 11, 19, 27,… CD = +8 Let n = the term number in the sequence Let A(n) = the value of the nth term in the sequence Value of term 1 = A(1) = 3 Value of term 2 = A(2) = A(1) + 8 = 3 + 8 = 11 Value of term 3 = A(3) = A(2) + 8 = 11 + 8 = 19 Value of term 4 = A(4) = A(3) + 8 = 19 + 8 = 27 Value of term n = A(n) = A(n - 1) + 8 The recursive formula for this sequence is

9. Writing a Recursive Formula Write a recursive formula for the given sequence 23, 35, 47, 59,… CD = +12 A(1) = 23 A(2) = A(1) + 12 = 23 + 12 = 35 A(3) = A(2) + 12 =35 + 12 = 47 A(4) = A(3) + 12 = 47 + 12 = 59 A(n) = A(n - 1) + 12 97, 88, 79, 70,… CD = -9 A(1) = 97 A(2) = A(1) - 9 = 97 - 9 = 88 A(3) = A(2) - 9 =88 - 9 = 79 A(4) = A(3) - 9 = 79 - 9 = 70 A(n) = A(n - 1) - 9 That was easy

10. More Writing Recursive Formulas Write a recursive formula for the given sequence 70, 77, 84, 91,… CD = +7 13, 10, 7, 4,… CD = -3 4.6, 4.7, 4.8, 4.9,… CD = +0.1 13, 5, -3, -11,… CD = -8 Asi De Facil

11. Explicit Formula An explicit formula is a function rule that relates each term of a sequence to the term number nth termfirst termterm numbercommon difference 16, 27, 38, 49,… CD = +11

12. Writing an Explicit Formula from a Recursive Formula

13. Homework Page 279: 30 - 40 Even Numbers

14. Writing an Recursive Formula from a Explicit Formula first termterm number common difference

15. More Writing an Recursive Formula from a Explicit Formula That was easy

16. Finding Specific Terms with an Explicit Formula Find the third, fifth, and thirteenth terms of the sequence described by each explicit formula.

17. More Finding Specific Terms with an Explicit Formula Find the third, fifth, and thirteenth terms of the sequence described by each explicit formula.

18. Homework Page 279 - 280: 42 - 52 Even Numbers