We think you have liked this presentation. If you wish to download it, please recommend it to your friends in any social system. Share buttons are a little bit lower. Thank you!
Presentation is loading. Please wait.
Published byKaitlin Cordle
Modified over 2 years ago
©Evergreen Public Schools Arithmetic Sequences Recursive Rules Vocabulary : arithmetic sequence explicit form recursive form 4/11/2011
©Evergreen Public Schools Practice Target Practice 7. Look for and make use of structure. Practice 7. Look for and make use of structure. Practice 8. Look for and express regularity in repeated reasoning.Practice 8. Look for and express regularity in repeated reasoning.
©Evergreen Public Schools Learning Target Sequences 3b I can write an arithmetic sequence in recursive form and translate between the explicit and recursive forms. Sequences 2 I can write an equation and find specific terms of an arithmetic sequence in explicit form.
©Evergreen Public Schools LaunchLaunch Yesterday, we completed the table and wrote an equation to find the area of L ( x ) = 2 x + 1
©Evergreen Public Schools LaunchLaunch With arithmetic sequence L ( x ) = 2 x + 1 L (4) = 9. Find the term follows L (4) L (100) = 201. Find the term follows L (100) Find the term follows L (x) Find the term comes before L ( x )
©Evergreen Public Schools ExploreExplore
7 Sequences from Unit 1 SeqRule L ( x ) 3, 5, 7, … L ( x ) = 2 x + 1 k ( x ) 17, 14, 11, … k ( x ) = We will learn this today. The rule in the 2 nd column is called the explicit rule. The rule in the 3 rd column is called the recursive rule.
©Evergreen Public Schools L ( x ) = 3, 5, 7, … explicit equation: L ( x ) = 2 x + 1 In the pattern L ( x ) the next term is 2 more than what I have now. Now is L ( x ) Next is L ( x +1) So rule is L ( x +1) =
©Evergreen Public Schools a ( x ) = 7, 9, 11, … explicit rule: a ( x ) = 2x + 5 The pattern in a is the next is 2 more than what I have now. Now is a ( x ) Next is a ( x +1) So rule is a ( x +1) = a ( x ) + 2 But wait, isn’t this the same rule for L ? L ( x +1) = L ( x ) + 2
©Evergreen Public Schools So the rule needs one more thing. What could that be? We need to know one term in the sequence. L ( x +1) = L ( x ) + 2 and L (1) = 3 k ( x +1) = a ( x ) – 3 and a (1) = 7
©Evergreen Public Schools For the sequence d ( x +1)= d ( x ) – 5 and d (1) = 63 Find the first four terms in the sequence. If d (20) = -33, find d (21) Write the explicit rule
©Evergreen Public Schools What if I wanted to write the rule with L ( x ) or k ( x ) instead of L ( x +1) or k ( x +1) ? L ( x ) = k ( x ) = L ( x ) and k ( x ) are what I have now. What other term do I need? I need what I had before. L ( x – 1) or k ( x – 1)? L ( x – 1) + 2 and L (1) = 3 k ( x – 1) + 2 and a (1) = 5
©Evergreen Public Schools Write rules for each of the sequences. SequenceExplicit Rule f ( x ) Recursive Rule f ( x + 1) f ( x ) add 3 __, 4, 7, 10, 13, f ( x ) = 3 x + 1 f ( x + 1) = f ( x ) +3 and f (1) = 4 g ( x ) 8, 14, 20, 26, … N ( x ) 34, 30, 26, 22, …
©Evergreen Public Schools Debra’s rules What do you think of Debra’s rules? Sequence f(x)f(x) f ( x ) 4, 7, 10, 13, … f(x) = f(x-1) + 3 and f(2) = 7 g ( x ) 8, 14, 20, 26, … g(x) = I(x-1) + 6 and I(4) = 26 N ( x ) 34, 30, 26, 22, … N(x) = N(x-1) – 4 and N(3) = 26
©Evergreen Public Schools Find the rate of change for each sequence. f(x)f(x) f ( x + 1) Rate of Change L(x) = L(x-1) + 2 and L(1) = 3 L(x+1) = L(x) + 2 and L(1) = 3 f(x) = f(x-1) + 3 and f(1) = 4 f(x+1) = f(x) + 3 and f(1) = 4 g(x) = g(x-1) + 6 and g(1) = 8 g(x+1) = g(x) + 6 and g(1) = 8 N(x) = N(x-1) – 4 and N(1) = 34 N(x+1) = N(x) – 4 and N(1) = 34 +2
©Evergreen Public Schools Common Difference 7, 11, 15, 19, 23 The rate of change is called the common difference, d in an arithmetic sequence. Why do you think it is called that? The first term of an arithmetic sequence, a 1 = 24 and the common difference d = 9. What are the first 5 terms of the sequence?
©Evergreen Public Schools Learning Target Did you hit the target? Sequences 3c I can write an arithmetic sequence in recursive form and translate between the explicit and recursive forms. Sequences 2a I can write an equation and find specific terms of an arithmetic sequence in explicit form.
©Evergreen Public Schools Practice
©Evergreen Public Schools Placemat Write a recursive rule for the sequence p(x) 4, 15, 26, 37, … Name 1 Name 2 Name 3 Name 4
©Evergreen Public Schools /11/2011 Arithmetic Sequences Explicit Rules Teacher Notes Notes : We will continue work students have done with arithmetic.
©Evergreen Public Schools /31/2011 Geometric Sequences Teacher Notes Notes: Have students complete the sequence organizer in the debrief Vocabulary:
©Evergreen Public Schools What is a Function Teacher Notes Notes: Today students will create their understanding of a function: “In a function each.
Recursive & Explicit Formulas January 5 – 7, 2010.
Patterns and sequences We often need to spot a pattern in order to predict what will happen next. In maths, the correct name for a pattern of numbers is.
Factoring Polynomials Grouping, Trinomials, Binomials, GCF & Solving Equations.
12/3/2010 ©Evergreen Public Schools Compare Graphs Teacher Notes Notes: The emphasis is on reading histograms, not making them. Record (on board.
©Evergreen Public Schools /31/2011 Systems of Inequalities Teacher Notes Supplies: Notes: Vocabulary:
1 The Other Vancouver Teacher Notes Supplies note paper and calculator Vocabulary formula This lesson is intended to have students see a purpose for rewriting.
Lesson: Linear and Recursive patterns objective: To find the n th term in a linear pattern. n th term is the expression that can be used to find any term.
1 6.4 Logarithmic Functions In this section, we will study the following topics: Evaluating logarithmic functions with base a Graphing logarithmic functions.
Unit 3A Multiple Choice Review!. Rate of Change EXPLICIT SEQUENCES ARITHMETIC Add/subtract GEOMETRIC multiply a n = d(n – 1) + a 0 d= common difference.
Holt CA Course Functions Warm Up Warm Up California Standards California Standards Lesson Presentation Lesson PresentationPreview.
1 Lesson Order of Operations. 2 Lesson Order of Operations California Standards: Algebra and Functions 1.3 Apply algebraic order of operations.
1 MA 1128: Lecture 15 – 6/17/13 Adding and Subtracting Rational Expressions (cont.)
21 st Century Lessons Evaluating Expressions Order of Operations 2 1.
ARITHMETIC SEQUENCES These are sequences where the difference between successive terms of a sequence is always the same number. This number is called the.
Holt Algebra Arithmetic Sequences 4-6 Arithmetic Sequences Holt Algebra 1 Warm Up Warm Up Lesson Presentation Lesson Presentation Lesson Quiz Lesson.
©Evergreen Public Schools /1/2011 Using a Graphing Calculator to Solve Systems of Equations Teacher Notes Supplies Needed: Graphing Calculator.
Slide 1 of 43 Slide 1 of 43 Conversion Problems 3.3.
1 Chapter 4 The while loop and boolean operators Samuel Marateck ©2010.
10/12/2014 ©Evergreen Public Schools Compare Strategies.
ADDING FRACTIONS You will need some paper! Fractions The top number is the numerator The bottom number is the denominator Example:2 numerator 5 denominator.
Introduction Exponential equations are equations that have the variable in the exponent. Exponential equations are found in science, finance, sports, and.
Objectives: Understand that algebraic operations follow the same rules as arithmetic operations. Solve simple equations Transform information from words.
Factors, Prime Numbers & Composite Numbers by Carol Edelstein.
Course Patterns and Sequences 1-7 Patterns and Sequences Course 1 Warm Up Warm Up Lesson Presentation Lesson Presentation Problem of the Day Problem.
10.2 Warm Up Warm Up Lesson Quiz Lesson Quiz Lesson Presentation Lesson Presentation Analyze Arithmetic Sequences and Series.
Introducing: common denominator least common denominator like fractions unlike fractions. HOW TO COMPARE FRACTIONS.
Everything you need to know about in grade 6 Number Patterns.
© 2016 SlidePlayer.com Inc. All rights reserved.