4.7: Arithmetic sequences I can write a recursive formulas given a sequence. Day 1

Describe a pattern in each sequence. Then find the next two terms. 7, 10, 13, 16 ___, ___, … 19 22 Add 3 3, 6, 12, ___, ___, … 24 48 Mult by 2 99, 88, 77, ___, ___, … 66 55 Subtract 11

Ex: 3, 5, 7, 9, … 2 Common difference for the above sequence: Arithmetic sequences: In an arithmetic sequence: The difference between each consecutive term is constant. This difference is called the common difference (d). Ex: 3, 5, 7, 9, … 2 Common difference for the above sequence:

If there is a common difference, what is it? 7, 10, 13, 16 ___, ___, … 19 22 3 3, 6, 12, ___, ___, … 24 48 Common difference: There isn’t one. 99, 88, 77, ___, ___, … 66 55 Common difference: -11

Is the following sequence arithmetic? If it is, describe the pattern. no Why not: I started with 5 and then multiplied by 2 each time. b. 5, 8, 11, 14… I started with 5 and then added 3 each time. yes c. 20, 5, -10, -25, … I started with 20 and then added -15 each time. yes

General term or nth term A(n-1)= Previous term An ordered list of numbers defined by a starting value (number) and a rule to find the general term. Recursive Formula: A(1) = first term A(n) = General term or nth term A(n-1)= Previous term Given the following recursive formula, find the first 4 terms. A(1) = 20 20, 26, 32, 38 A(n) = A(n-1) + 6 1st term 2nd term 3rd term 4th term Think: previous term + 6 Given the following recursive formula, find the first 4 terms. A(1)= -18 -18, -21, -24, -27, 1st term 2nd term 3rd term 4th term A(n) = A(n-1) - 3 Think: previous term -3

Write a recursive formula for each sequence. (always has two parts) 7, 10, 13, 16, … 7 Recursive rule: 7 A(1) = ______ A(1) = ____ +3 A(n) = A(n-1)_____ A(n) = A(n-1) + d A(1) = 7 A(n) = A(n-1) + 3 3 3, 9,15, 21,… 97, 87, 77, 67 … A(1) = 3 A(n) = A(n-1) + 6 3 A(1) = A(1) = 97 + 6 A(n) = A(n-1) A(n) = A(n-1) - 10 Homework: pg 279: 9-35