# 090799768954

2 de Nov de 2022                                                                       1 de 71

### 090799768954

• 1. FIRST QUARTER MATHEMA TICS MELC: Generates patterns…
• 3. In History, Philip pine Asian World In Biology, Cells Tissue s Organs In Essay Writing, Introduc tion Body Conclusi on
• 4. Learn Mathematics online, the best ways we can
• 5. 1. find the pattern of a sequence. 2. identify the next term of a sequence. 3. differentiate between infinite and finite sequences. 4. give the value of sum of numbers in a sequence 5. value the importance of respect in a family and orderliness in workplace. Learn Mathematics online, the best ways we can At the end of this course presentation, you will be able to:
• 7. Sequence A succession of numbers in a specific order 1, 2, 3, 4, 5,…
• 9. Where can sequence be observed in daily living? Learn Mathematics online, the best ways we can
• 10. Where can sequence be observed in your own home? Learn Mathematics online, the best ways we can
• 11. Where can sequence be observed in a specific household chore? Learn Mathematics online, the best ways we can
• 13. Term 1, 2, 3, 4, 5 numbers in the sequence 1st term 5th / last term
• 14. Types of Sequences
• 15. Finite Sequence a sequence that ends {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} +1 +1 +1 +1 +1 +1 +1 +1 +1 < A sequence that has a first term and a last term > limited domain
• 16. Finite Sequence
• 17. Infinite Sequence when the sequence goes on forever it is called an infinite sequence {1, 2, 3, 4, 5, …} ellipsis <There is another term, after each term of the sequence> infinite domain
• 18. Determine… 1. 1, 4, 16, 25, … , 81 2. 8, 16, 24, 32. … 3. 1, 4,7,10,13, … 4. 6, 12, 18, 24, … , 60 5. 1,5, 9, 13, 17, …
• 20. General terms of sequences If a is a sequence, its general term or nth term is its function value a(n) usually denoted by an (read as “a sub n”)
• 21. In the sequence 0, 1, 3, 6, 10, 15,… we can denote the terms as follows: a₁ = 0 a₂ = 1 a₃ = 3 a₄ = 6 a₅ = 10 a₆ = 15 1st term 2nd term 3rd term 4th term 5th term 𝑎1 𝑎2 𝑎3 𝑎4 𝑎5 6th term 7th term 8th term 9th term 10th term 𝑎6 𝑎7 𝑎8 𝑎9 𝑎10 nth term 𝑎𝑛
• 22. Find the first four terms of the sequence defined by an = 2n + 1 first term Replace n with 1, 2, 3, and 4 in the expression of an a₁ = 2(1) + 1 = 3 second term a₂ = 2(2) + 1 = 5 third term a₃ = 2(3) + 1 = 7 20th term a₄ = 2(4) + 1 = 9 an = 2n + 1 = 3, 5, 7, 9 fourth term A₂₀ = 2(20) + 1 = 41
• 23. an = 𝒏+𝟐 𝒏+𝟒 Find the first five terms a₁ = 𝟑 𝟓 a₂ = 𝟐 𝟑 a₃ = 𝟓 𝟕 a₄ = 𝟑 𝟒 a₅ = 𝟕 𝟗 a₂₅= 𝟐𝟕 𝟐𝟗 a₃₇= 𝟑𝟗 𝟒𝟏 A₇₃= 𝟕𝟓 𝟕𝟕
• 24. Find the indicated term of each sequence 1. an = 6n - 4 = 50 a₉ 2. an = 1 - 𝟏 𝒏 = 𝟏𝟏 𝟏𝟐 a₁₂ 3. an = (𝟒)𝒏−𝟑 ( n + 2) = 112 a₅ 4. an = (−𝟐)𝒏−𝟓 = 256 a₁₃ 5. an = 7n + 7 = 77 a₁₀
• 26. Sequence A succession of numbers in a specific order
• 27. Term 1, 2, 3, 4, 5 numbers in the sequence 1st term 5th / last term
• 28. Types of Sequences Finite sequence Infinite sequence
• 29. Finite Sequence a sequence that ends limited domain
• 30. Infinite Sequence a sequence goes on forever infinite domain
• 31. General terms of sequences nth term = function value is a(n) usually denoted by an (read as “a sub n”)
• 32. The general term of a sequence is given. Write the first four terms, the 10th term, and the 15th term 1. an = 2n -1 = 1, 3, 5, 7 ; 19; 29 2. an = 3n + 2 = 5, 8, 11, 14; 32; 47 3. an = n² + 2= 3, 6, 11, 18; 102;227 4. an = n² - 3 = -2, 1, 6, 13; 92 ; 222 5. an = 𝒏 𝒏+𝟏 = 𝟏 𝟐 , 𝟐 𝟑 , 𝟑 𝟒 , 𝟒 𝟓 ; 𝟏𝟎 𝟏𝟏 ; 𝟏𝟓 𝟏𝟔
• 33. The general term of a sequence is given. Write the first four terms, the 10th term, and the 15th term 6. an = 𝒏 𝒏+𝟒 = 𝟏 𝟓 , 𝟏 𝟑 , 𝟑 𝟕 , 𝟏 𝟐 ; 𝟓 𝟕 ; 𝟏𝟓 𝟏𝟗 7. an = 1 + 𝟏 𝒏 = 2 , 𝟑 𝟐 , 𝟒 𝟑 , 𝟓 𝟒 ; 𝟏𝟏 𝟏𝟎 ; 𝟏𝟔 𝟏𝟓
• 34. The general term of a sequence is given. Write the first four terms, the 10th term, and the 15th term 8. an = 1 - 𝟏 𝒏 =0, 𝟏 𝟐 , 𝟐 𝟑 , 𝟑 𝟒 ; 𝟗 𝟏𝟎 ; 𝟏𝟒 𝟏𝟓 9. an = 𝒏 −𝟏 𝒏+𝟐 = 0 , 𝟏 𝟒 , 𝟐 𝟓 , 𝟏 𝟐 ; 𝟑 𝟒 ; 𝟏𝟒 𝟏𝟕 10. an = 𝒏+𝟐 𝒏+𝟑 = 𝟑 𝟒 , 𝟒 𝟓 , 𝟓 𝟔 , 𝟔 𝟕 ; 𝟏𝟐 𝟏𝟑 ; 𝟏𝟕 𝟏𝟖
• 35. Find the indicated term of each sequence 1. an = 8n - 18 = 78 a₁₂ 2. an = 2n + 5 =33 a₁₄ 3. an = (−𝟐)𝒏−𝟐 (2n + 1) = 208 a₆ 4. an = (1 - 𝟏 𝒏 ) = 𝟗 𝟏𝟎 a₁₀
• 36. First Quarter seatwork Date Seatwork # & name Score 08 – 08 - 2022 Seatwork no. 1 – Sequence 25 / 25
• 38. Find the indicated term of each sequence 1. an = 3n - 4 = 32 a₁₂ 2. an = 6n + 5 =89 a₁₄ 3. an = (−𝟑)𝒏−𝟏 (n + 1) = - 1701 a₆ 4. an = (1 - 𝟏 𝒏 )² = 𝟏𝟒 𝟏𝟓 a₁₅ 5. an = 𝒏 −𝟑 𝒏+𝟐 = 𝟕 𝟏𝟐 a₁₀
• 40. Write formulas for sequences
• 41. Recursive Form The general term is expressed by using the previous term. 2, 5, 8, 11, 14 𝑎𝑛 = 𝑎𝑛−1 + 3 𝑎6−1 + 3 𝑎6 = = 𝑎5 + 3 = 17 = 14 + 3 6th 𝑡𝑒𝑟𝑚
• 42. Recursive Form Learn Mathematics online, the best ways we can The general term is expressed by using the previous term. 18, 14, 10, 6, 2, -2 𝑎𝑛 = 𝑎𝑛−1 − 4
• 43. Recursive Form Learn Mathematics online, the best ways we can The general term is expressed by using the previous term. 1, 3, 9, 27, 81 𝑎𝑛 = 𝑎𝑛−1 𝑥3 𝑎𝑛 = 3(𝑎𝑛−1)
• 44. Find for the Recursive Form. 1, 3, 7, 15, 31, 63 𝑎𝑛 = 2(𝑎𝑛−1) + 1 multiply previous term by 2 add 1
• 45. Recursive Form Learn Mathematics online, the best ways we can The general term is expressed by using the previous term. 3, 7, 11, 15, 19 𝑎𝑛 = 𝑎𝑛−1 +4
• 47. Explicit Form The general term is expressed by using the position of the term in the sequence. Express the sequence into another formula. 2, 4, 6, 8, 10, … Express it through a table first. Term (𝒂𝒏) 2 4 6 8 10 Position (𝑛) 1 (1st) 2 (2nd) 3 4 5
• 48. Use the position in getting the formula of the general term. Term (𝒂𝒏) 2 4 6 8 10 Position (𝑛) 1 (1st) 2 (2nd ) 3 (3rd ) 4 (4th) 5 (5th) 𝑎𝑛 = (𝑛) 2 Explicit Form To get 2, multiply the first term (1) by 2 To get 4, multiply the second term (2) by 2 To get 6, multiply the third term (3) by 2
• 49. Explicit Form 3, 6, 9, 12, 15, 18 𝑎𝑛 = 3𝑛 Term (𝒂𝒏) 3 6 9 12 15 Position (𝑛) 1 2 3 4 5
• 50. Explicit Form The general term is expressed by using the position of the term in the sequence. 5, 10, 15, 20 𝑎𝑛 = 5𝑛
• 51. 1, 4, 9, 16, 25,… 𝑎𝑛 = n² Term (𝒂𝒏) 1 4 9 16 25 Position (𝑛) 1 2 3 4 5
• 52. 2, 5, 10, 17, 26,… 𝑎𝑛 = n² + 1 Term (𝒂𝒏) 2 5 10 17 26 Position (𝑛) 1 2 3 4 5 𝑎𝑛 = 2n 𝑎𝑛 = 2n + 1 𝑎𝑛 = n² 𝑎𝑛 = n² + 1
• 53. 1, 4, 7, 10, 13,… 𝑎𝑛 = 3n − 2 Term (𝒂𝒏) 1 4 7 10 13 Position (𝑛) 1 2 3 4 5 𝑎𝑛 = n² 𝑎𝑛 = 2n − 1 𝑎𝑛 = 3n 𝑎𝑛 = 3n – 2
• 54. Explicit Form 10, 15, 20, 25, 30, … 𝑎𝑛 = 5(𝑛 + 1)
• 55. Find the Explicit Form. Learn Mathematics online, the best ways we can 12, 16, 20, 24, 28, … 𝑎𝑛 = 4(𝑛 + 2)
• 56. Find a possible formula for the general terms of the sequence a. 1, 8, 27, 64, 125,… an = n³ b. 2, 4, 6, 8, 10, 12,… an = 2n c. 1, 3, 5, 7, 9,11,… an = 2n - 1
• 58. Fibonacci Sequence The next number is obtained by adding the previous two terms Fibonacci Pattern
• 59. What are the next three numbers after the sequence? 1, 1, 2, 3, 5, 8, … 13 21 34 + + + + +
• 60. Leonardo Pisano Bigollo -born in Pisa, Italy -a famous Italian Mathematician of the Medieval Period -famous for his work, Liber Abaci Leonardo Pisano Bigollo
• 61. Fibonacci Pattern -it is a pattern used in taking photos in a great manner Fibonacci Pattern -uses a proper concentration of the foreground against the background
• 62. Fibonacci Pattern
• 63. Fibonacci Pattern Golden ratio
• 64. Learn Mathematics online, the best ways we can
• 65. Learn Mathematics online, the best ways we can
• 66. Learn Mathematics online, the best ways we can
• 70. chsths.aralinks.net  My Subjects  Math 10 Faith  First Quarter  Seatwork no. 1 (follow the instruction)

### Notas del editor

1. What would happen if there are no patterns, routines or guidelines? Why do we need patterns routines or guidelines?