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Pattern & Sequence

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Jasmin Tawantawan-Pangilamun

This document discusses patterns and sequences in mathematics. It provides examples of different types of patterns and sequences found in nature as well as number patterns like arithmetic, geometric, and Fibonacci sequences. Formulas are given for exponential growth, arithmetic sequences, geometric sequences, and the Fibonacci sequence, along with examples of using the formulas to analyze patterns and sequences.

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Mathematics In the Modern World (Nature of Mathematics JASMIN C. TAWANTAWAN, LPT, Ph.D (CAR)
Pattern are regular, repeated, or recurring forms or designs. 2
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Nature forms of pattern 4
Roadmap 5 1 3 5 6 4 2 Snowflakes and Honeycombs Tigers stripe and hyenas Spots Snails shell Order of rotation Sunflower Flower petals 5 World population
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Formula of exponential growth: = 倹 Where, A - is the size of the population after in grows P - is the initial number of people r - is the rate of growth, and t - is time e is Eulers constant . 13
This is a slide title Example: The exponential growth model = 300.02 describes the population of a city in the Philippines in thousands, t year after 1995. a. What is the population of the city in 1995? b. What will be the population in 2017? 14
Sequence is an order list of numbers, called terms, that may have repeated values. The arrangement of these terms is set by definite rule. Sequence Example: Analyze the given sequence for its rule and identify the next three terms. a. 1, 10, 100, 1000 b. 2,5,9,14, 20 15
Types of Number Patterns in Math 1. Arithmetic sequence An arithmetic sequence is a sequence where every term after the first is obtained by adding a constant called the common difference. In general the nth term of a given sequence: = + = ( + ) Example: 1. What is the 12th term of the arithmetic sequence 0, 5, 10, 15, 20, 25,? 2. Find the sum of arithmetic sequence 0, 5, 10, 15, 20, 25. 16
2. 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. = . Example. Find the common ratio of the sequence 32, 16, 8, 4, 2, ... . 17
3. Fibonacci Sequence The Fibonacci sequence is defined by the recursive formula = + , = = Example 1. Given the recursive formula for the Fibonacci sequence 告 = 告2 + 告1, も 1 = 2 = 1. a. 3 b. 4 18
Mathematics for our world Mathematics for Organization Ex. Sales, internet, social media, growth, ideas, data, & etc. Mathematics for Prediction Ex. Applying concept of probability, historical pattern, metrological, weather, & etc. Mathematics for Control Ex. Gravitational waves, threat of climate change 19
Thanks! Any questions? 20
21 Activity 1 Determine what comes next in the given pattern. 1. A, C, E, G, I, ______ 2. 15, 10, 14, 10, 13, 10, ____ 3. 3,6,12,24,48,96,____ 4. 27,30,33,36,39,_____ 5. 41,30,37,35,33,____ Find the missing quantity. 1. = 680,000; = 12% ; = 8 2. = 1,240,000; = 8% ; = 30

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Pattern & Sequence

  • 2. Pattern are regular, repeated, or recurring forms or designs. 2
  • 3. 3
  • 5. Roadmap 5 1 3 5 6 4 2 Snowflakes and Honeycombs Tigers stripe and hyenas Spots Snails shell Order of rotation Sunflower Flower petals 5 World population
  • 6. 6
  • 7. 7
  • 8. 8
  • 9. 9
  • 10. 10
  • 11. 11
  • 12. 12
  • 13. Formula of exponential growth: = 倹 Where, A - is the size of the population after in grows P - is the initial number of people r - is the rate of growth, and t - is time e is Eulers constant . 13
  • 14. This is a slide title Example: The exponential growth model = 300.02 describes the population of a city in the Philippines in thousands, t year after 1995. a. What is the population of the city in 1995? b. What will be the population in 2017? 14
  • 15. Sequence is an order list of numbers, called terms, that may have repeated values. The arrangement of these terms is set by definite rule. Sequence Example: Analyze the given sequence for its rule and identify the next three terms. a. 1, 10, 100, 1000 b. 2,5,9,14, 20 15
  • 16. Types of Number Patterns in Math 1. Arithmetic sequence An arithmetic sequence is a sequence where every term after the first is obtained by adding a constant called the common difference. In general the nth term of a given sequence: = + = ( + ) Example: 1. What is the 12th term of the arithmetic sequence 0, 5, 10, 15, 20, 25,? 2. Find the sum of arithmetic sequence 0, 5, 10, 15, 20, 25. 16
  • 17. 2. 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. = . Example. Find the common ratio of the sequence 32, 16, 8, 4, 2, ... . 17
  • 18. 3. Fibonacci Sequence The Fibonacci sequence is defined by the recursive formula = + , = = Example 1. Given the recursive formula for the Fibonacci sequence 告 = 告2 + 告1, も 1 = 2 = 1. a. 3 b. 4 18
  • 19. Mathematics for our world Mathematics for Organization Ex. Sales, internet, social media, growth, ideas, data, & etc. Mathematics for Prediction Ex. Applying concept of probability, historical pattern, metrological, weather, & etc. Mathematics for Control Ex. Gravitational waves, threat of climate change 19
  • 21. 21 Activity 1 Determine what comes next in the given pattern. 1. A, C, E, G, I, ______ 2. 15, 10, 14, 10, 13, 10, ____ 3. 3,6,12,24,48,96,____ 4. 27,30,33,36,39,_____ 5. 41,30,37,35,33,____ Find the missing quantity. 1. = 680,000; = 12% ; = 8 2. = 1,240,000; = 8% ; = 30