agenda 10 MIN Go over benchmark 30 MIN Unit 2 Day 1 Notes 5 MIN Mastery Work

Transcription

1 Welcome! Today you will need: *a graphing calculator *a new packet *your name tag *a chrome book for HW (later) agenda 10 MIN Go over benchmark 30 MIN Unit 2 Day 1 Notes 5 MIN Mastery Work

2 remember Smart is not what you are. It is what you work to become. -Unknown unıt 2: lınear models & sequences 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 I can write the recursive formula for an arithmetic sequence. I can read and write recursive formulas with subscript notation. I can find terms of a sequence given recursively.

3 Fri 9/15 Mon 9/18 Tue 9/19 Wed 9/20 Thu 9/21 Fri 9/22 Mon 9/25 Tue 9/26 Vocabulary: Defn of Sequence: an ordered list of numbers Each number in a sequence is called a. Arithmetic Sequence: is a sequence where each term is just the previous term a constant. The constant is called the

4 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, These sequences are RECURSIVE. Recursion: where each step of a pattern is on the step or steps before it. Recursive Formula: Creates sequence & contains the following pieces: Starting value: The first number in the series. u 1 Recursive rule: defines the n th term in relation to the previous term (or terms) u n = u n 1 + Condition: tells which values of n the rule will work for.

5 Let's come up with a recursive formula to show the following pattern and find the next 3 terms. ex) 5, 8, 11,,, Recursive Routine How are you doing with this?

6 Is there a way to do this on my calculator? ex) 5, 8, 11,,, Recursive Routine Calculator u 1 = 5 5 enter ans + 3 enter, enter, enter... u n = u n You MUST count carefully. Use this to find the 15th term!

7 What if I don't want to count or lose track while counting? ex) 5, 8, 11,,, Recursive Routine Calculator u 1 = 5 u n = u n {1, 5} enter {Ans (1)+1, Ans (2) +3} enter enter...

8 Let's write a recursive formula for pattern A. u 4 = 10 u 5 = 12 u 1 = 4 u 2 = 6 u 3 = 8 u n = u n where n > 1 u n = 2n + 2 where n > 1 Find: next 3 terms u 15 = u = 28 Let's write a recursive formula for pattern B. u 4 = 12 u 5 = 15 u 1 = 3 u 2 = 6 u 3 = 9 Find: next 3 terms u n = u n where n > 1 u 10 = u n = 3n where n > 1 u = 36

9 Let's write a recursive formula for pattern C. u 2 = 10 u 1 = 7 u 4 = 16 u 5 = 19 u 3 = 13 u n = u n where n > 1 Find: next 3 terms u 20 = u n = 3n + 4 where n > 1 u = 40 Let's write a recursive formula for pattern D. u 1 = 7 u 2 = 14 u 3 = 21 u 4 = 28 u 5 = 35 u n = u n where n > 1 u n = 7n where n > 1 Find: next 3 terms u 32 = u = 70

10 Let's write a recursive formula for pattern E. u 4 = 31 u 5 = 39 u 1 = 7 u 2 = 15 u 3 = 23 u n = u n where n > 1 u n = 8n 1 where n > 1 Find: next 3 terms u 12 = u = 71 Did you meet the goal? I can define orally and in writing: sequence, term (u 1 ), general term (u n ), recursive formula, recursive rule, arithmetic sequence, common difference I can write the recursive formula for an arithmetic sequence. I can read and write recursive formulas with subscript notation. I can find terms of a sequence given recursively. Mastery Work: (on Google Classroom) pg #1ab; 3 4; 5ab; 6 8; 10

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13 ACT Openers: Linear Algebra [1] If x is an integer and y = -3x + 7, what is the least value of x for which y is less than 1? [A] 1 [B] 2 [C] 3 [D] 4 [E] 5 [2] Which of the following is the simplified form of the expression 5(x - 3) - 3x + 10? [A] 2x - 5 [B] 5x + 7 [C] 8x - 5 [D] 12x + 10 [E] 22x welcome 1. Take out notebook, pencil and calculator 2. Take out assignment from yesterday 3. Complete the Warm up. Warm up: Write a recursive routine for the following and find the 10th term 15, 11, 7, 3,... R.R. 10th term A concert hall has 59 seats in Row 1, 63 seats in Row 2, 67 seats in Row 3, and so on. The concert hall has 35 rows of seats. R.R. Seats in row 6

14 agenda 05 MIN Warm Up 05 MIN Homework?'s 20 MIN 15 MIN Mastery Worksheet