Math10 Quarter 1 Wk1 Generating Patterns
- 1. SEQUENCE
- 2. At the end of the lesson, the learners should be able to: 01 Define sequence 02 Write the next term in a sequence 03 Give examples of sequence in real life
- 3. SEQUENCE It is a set of objects which is listed in a specific order, one after another. Each member or element in the sequence is called term.
- 4. 1, 2, 3, 4, 5 𝒂𝟏 𝒂𝟐𝒂𝟑𝒂𝟒𝒂𝟓 First term Second term Third term Fourth term Fifth term SEQUENCE
- 6. Finite Sequence It is a sequence which contains a limited number of terms. Example 1: a) b)
- 7. Infinite Sequence It is a sequence which contains a COUNTLESS number of terms. The number of terms of the sequence continues without stopping or it has no end term. Example 2: a) b)
- 8. Infinite Sequence The ELLIPSIS (…) at the end shows that the sequences are infinite.
- 9. General Term or nth Term
- 10. General Term or the nth Term It is an algebraic expression which is denoted by () that relates the term to its position number in the sequence. It is also called explicit formula.
- 11. General Term or the nth Term Find the first four terms of the sequence . Example 3:
- 12. General Term or the nth Term Find the 5th and the 8th term of the sequence . Example 4:
- 13. GROUP ACTIVITY
- 14. QUESTION 1 QUESTION 2 QUESTION 3 QUESTION 4
- 15. QUESTION 1 Write the first four terms of the sequence .
- 16. QUESTION 2 Write the first four terms of the sequence .
- 17. QUESTION 3 Write the first four terms of the sequence .
- 18. QUESTION 4 Write the first four terms of the sequence .
- 19. What did you learn? 1) A sequence is a set of objects which is listed in a specific order, one after another. 2) A term is a member or element in the sequence . 3) A finite sequence contains a limited number of terms while infinite sequence contains a countless number of terms.
- 20. ASSESSMENT 1) Which of the following shows a pattern? A) 3, 2, 3, 2, 3, 2 B) 5, 7, 2, T, 6, Y C) A, G, M, T, 0, 9 D) smooth, long, wall, sing
- 21. ASSESSMENT 2) Which of the following defines infinite sequence? A) Days of the week B) Teenage life C) Every other day D) First Fridays of July 2020
- 22. ASSESSMENT 3) What are the next three terms of the sequence 0, 1, 1, 2, 3, 5, …? A) 5, 5, 5 B) 8, 13, 21 C) 7, 9, 11 D) 11, 11, 13
- 23. ASSESSMENT 4) What is the 11th term in the sequence -1, 4, -9, 16, -25, …? 5) Find the first three terms of the sequence .
- 24. FINDING THE GENERAL TERM, GIVEN SEVERAL TERMS OF THE SEQUENCE
- 25. At the end of the lesson, the learners should be able to: 01 Identify the pattern in a sequence 02 Write the general term given several terms of the sequence
- 26. Example 1: Write the general term of the sequence 5, 12, 19, 26, 33, … 5, 12, 19, 26, 33, … +7 +7 +7 +7
- 27. 5, 12, 19, 26, 33, … +7 +7 +7 +7 Term Given Pattern 1 5 2 12 3 19 4 26 5 33
- 28. Example 2: Write an expression for the term of the sequence 1, -1, 1, -1, 1, … 1, -1, 1, -1, 1, … ×(−1) ×(−1) ×(−1) ×(−1)
- 29. Term Given Pattern 1 1 2 -1 3 1 4 -1 5 1 1, -1, 1, -1, 1, … ×(−1) ×(−1)×(−1) ×(−1)
- 30. Example 3: Write tgeneral term of the sequence 2, 4, 8, 16, 32, … 2, 4, 8, 16, 32, … ×2 ×2 ×2 ×2
- 31. Example 4: Find the general term of the sequence 1 1 , 1 4 , 1 9 , 1 16 , 1 25 , … PERFECT SQUARES
- 33. Write an expression for the term of the given sequence.
- 34. General Term
- 35. General Term
- 36. Term Given Pattern 1 2 2 4 3 8 4 16 5 32 2, 4, 8, 16, 32, … ×2 ×2×2×2 General Term 𝑎𝑛=2𝑛
- 37. Term Given Pattern 1 2 3 4 5 1 1 , 1 4 , 1 9 , 1 16 , 1 25 , … General Term 𝑎𝑛= 1 𝑛 2
Editor's Notes
- #1: Pupunta ako ng Boracay, magdadala ako ng: Ikaw, anong dadalhin mo,
- #8: Sometimes a pattern in the sequence can be obtained and the sequence can be written using a general term.
- #20: Sometimes a pattern in the sequence can be obtained and the sequence can be written using a general term.
- #21: Sometimes a pattern in the sequence can be obtained and the sequence can be written using a general term.
- #22: b
- #23: -121 5, 9, 11,