1st Quarter Mathematics Lesson 1 PDF

What can you say about the photo? What can you say about the photo? 1, 8, 27, 64, 125 What can you say about the numbers above? INTRODUCTION TO SEQUENCES 1st Quarter Mathematics Lesson 1 LEARNING GOALS: At the end of the discussion, I can… define a sequence. differentiate arithmet...

What can you say about the photo? What can you say about the photo? 1, 8, 27, 64, 125 What can you say about the numbers above? INTRODUCTION TO SEQUENCES 1st Quarter Mathematics Lesson 1 LEARNING GOALS: At the end of the discussion, I can… define a sequence. differentiate arithmetic from geometric sequence. relate patterns/ sequence to the teachings of Jesus and apply it to my everyday life.  WITH PATTERN OR WITHOUT? Instructions: Identify if each picture below shows a pattern or not. If there is a pattern. If the pattern continues, identify the next term. WITH PATTERN OR WITHOUT? Color of the Triangles and its orientation: Blue-up, Yellow-down, Yellow-done, Blue-up, Yellow- down, Yellow-down, Blue-up, Yellow-down, _________ WITH PATTERN OR WITHOUT? Color of the Banderitas: Red, Yellow, Green, Blue, Red, Yellow, Green, Blue, Red, _____ WITH PATTERN OR WITHOUT? Days in the Calendar: 1, 3, 5, 7, ___ WITH PATTERN OR WITHOUT? Number of Coffee Beans: 4, 6, 8, _____  The set objects in our short activity are called sequences. A sequence is an ordered set of numbers formed according to some pattern or rule. A sequence, denoted by {𝑎𝑛 } is a function whose domain is the set of positive integers or a finite subset of positive integers.  1, 3, 5, 7, … , 𝒶𝑛 ,... 𝒶1 is called the first term 𝒶2 is called the second term 𝒶𝑛 is called the nth term or the general term WHAT IS A SEQUENCE ? A sequence is a function whose domain is the finite set {1, 2, 3,..., n} or the infinite set {1, 2, 3,...} Example: {1, 9, 17, 25, 33, 𝐴6 , 𝐴7 } TERMS Term Value of the term 1 9 17 25 33  ARITHMETIC SEQUENCE An arithmetic sequence is a sequence where every term after the first term is obtained by adding a constant called the common difference. Example: 1, 4, 7, 10.... The common difference is 3 The fifth term is 13. ARITHMETIC SEQUENCE Ex #2: 3, 8, 13, 18.... The common difference is ____ The fifth term is ____ ARITHMETIC SEQUENCE Ex #3: The common difference could also be negative 25, 23, 21, 19,.... The common difference is ____ The fifth term is ____ ARITHMETIC SEQUENCE Ex #4: 4, 9, 14, 19,.... The common difference is ____ The seventh term is ____ ARITHMETIC SEQUENCE Ex #5: 41, 27, 13, -1,.... The common difference is ____ The sixth term is ____ WHAT’S NEXT? Each item below shows a pattern. Identify the next number/ term. 1. 0, 4, 8, 12, 16, ______, ______ 2. 9, 4, -1, -6, -11, _____, ______ 2 7 5 13 3. , , , , _____, ______ 3 6 3 6  GEOMETRIC SEQUENCE A geometric sequence is a sequence where each term after the first is obtained by multiplying the preceding term by a nonzero constant called the common ratio. The common ratio (r) can be determined by dividing any term in the sequence by the term that precedes it. Example: 1, 3, 9, 27, … The common ratio is 3 The fifth term is 81.  GEOMETRIC SEQUENCE Ex # 2: 2, 6, 18, 54, … The common ratio is ____ The fifth term is ____. GEOMETRIC SEQUENCE Ex # 3: 1, -2, 4, -8, … The common ratio is ____ The sixth term is ____.  GEOMETRIC SEQUENCE Ex # 4: The common ratio can also be less than 1 but not 0. 5 5 10, 5, , … 2 4 The common ratio is ____ The sixth term is ____. LEARNING GOALS: At the end of the discussion, I can… define a sequence. differentiate arithmetic from geometric sequence. relate patterns/ sequence to the teachings of Jesus and apply it to my everyday life. TRY THIS!! Study the following patterns then supply the missing term/s to complete the sequence. 1. 5, 8, 11, 14, ______, ______, …. 2. ½, 1, 3/2, 2, _______, ______, _____, … 3. 3, -6, 12, ______, _______, -96, …. 4. 3/7, -6/35, ______, _______, -69/35, …. 5. 12, 9, 27/4, ______, …..