Mapeh 10 lesson 1 quarter 1 10 Germany m

Mapeh 10 lesson 1 quarter 1 10 Germany m

• 1.
  ARITHMETIC SEQUENCE
• 2.
  Let’s think! •The SSGClub proposed a project on collecting bottles to lessen the trash on our school. If the officers can collect 25 bottles on the first day, 45 on the second day , 65 on the third day, and the pattern continues, how many bottles can they collect in the fifth day? How many bottles they will collect in one week?
• 3.
  Arithmetic Sequence •Is anordered set of numbers that have a common difference between each consecutive term.
• 4.
  Common difference • Itis the value between each successive number in an arithmetic sequence. • the formula to find the common difference of an arithmetic sequence is: d = a(n) - a(n - 1) • where a(n) is nth term in the sequence, and a(n - 1) is the previous term or (n - 1)th term) in the sequence.
• 5.
  •1. 2, 4,6, 8, ___.... •2. 7, 9, 11, ___, ___, 17, 19 •3. 1, 8, 27, 64, 125, ____... •4. 5, 10, 7, 14, 11, 22, 19, ___
• 6.
  Tell if thefollowing sequences is an arithmetic sequence or NOT, if an arithmetic sequence find its common difference. • 1.) 2, 4, 6, 11, .... • 2.) 7, 10, 13, 16, 19,… • 3.) 4, 8, 16, 32, … • 4.) 2, 6, 10, 14, … • 5.) 2, 5, 10, 17, … • 6.) 1, 8, 9, 16, … • 7.) 2, 11, 20, 29, …
• 7.
  Arithmetic Sequence • Thenth term of an arithmetic sequence with first term a1 and common difference d is given by: • an = a1 + d (n-1) • where: • an is the term that corresponds to nth position, • a1 is the first term; and • d is the common difference
• 8.
  Let’s apply! • A.Find the 21st term of the arithmetic sequence: 6, 9, 12, 15,… • Solution: • a. From the sequence, 𝑎1 = 6 , d = 3, and n = 21. • b. Using the formula, substitute these values. • a21 = 6 + 3 (21 – 1) • a21 = 6 + 3 (20) • a21 = 6 + 60 • a21 = 66 • c. Thus, the 21st term is 66.
• 9.
  Let’s apply! • B.Find an for each of the following arithmetic sequence. • 1. a1 = 5; d = 4 ; n = 11 • 2. a1 = 14; d = –3 ; n = 25 • 3. a1 = 12; d = ½; n = 16 • 4. –10, –6, –2, 2, 6, … n = 27 • 5. 3, 5/2, 2, 1/2 ,0,… n = 28
• 10.
  Activity: Find theterm named of the following arithmetic sequence. • 1.) 2, 9, 16, 23, ...., Find a40 • 2.) 7, 10, 13, 16, 19,…, Find a82 • 3.) 2, 6, 10, 14, …, Find a104 • 4.) 2, 11, 20, 29, …, Find a56 • 5.) 7, 4, 1, -2, -5,…, Find a78 • 6.) -3, 2, 7, 12, 17,…, Find a98 • 7.) -10, -12, -14, -16,..Find a312
• 11.
  Solving Unknown Values inArithmetic Sequence
• 12.
  Examples: • 1. Inthe arithmetic sequence: 7, 10, 13, 16, . . .; find n if an = 304. • Solution: • a. From the sequence, a1 = 7, d = 3, and an = 304. • b. Using the formula, substitute these values. • an = a1 + d (n-1) • 304 = 7 + 3 (n – 1) • 304 = 7 + 3n – 3 • 304 = 4 + 3n • 300 = 3n • n = 100 • c. Thus, 304 is the 100th term of the sequence.
• 13.
  Example
• 14.
  Examples: • B. Findthe first term in the arithmetic sequence where the 35th term is 687 and the common difference 14. • Using arithmetic sequence formula, • an = a1 + (n − 1)d • 687 = a1 + (35 - 1)14 • 687 = a1 + (34)14 • 687 = a1 + 476 • a1 = 211 • Answer: The first term in the sequence is 211.
• 15.
  Examples: • C. The3rd term of an arithmetic sequence is 8 and the 16th term is 47. Find d, 𝑎1 and the 71st term. • Solution: a. From the sequence, a3 = 8 and a16 = 47 • b. These imply that: • a3 = a1 + d (3-1) a16 = a1 + d (16-1) • 8 = a1 + d (3-1) 47 = a1 + d (16-1) • 8 = a1 + 2d Eq. 1 47 = a1 + 15d Eq. 2
• 16.
  C. Continuation
• 17.
  C. Continuation