Formulating Rules for sequence.pptx
- 1. Formulating Rules for sequence
- 2. Part I: Study the following sequences below. Write the rule describing each sequence. Sequence nth Term Rule 1.) 3,6,9,12... 2.) 1,4,9,16... 3.) y,𝑦2, 𝑦3, 𝑦4... 4.) 2,5,8,11... 5.) 2,4,6,8…. 3n 𝒏𝟐 𝒚𝒏 3n-1 2n
- 3. Sequence The next three term 6. 5, 7 , 9, 11 7. 15, 18, 21, 24 8. 3, 8, 18, 38 9. 7, 10, 13, 16, 10. 18, 27, 36, 45, 13, 15, 17, 27, 30, 33 78, 158, 318 19, 25 22, 54, 63, 72
- 4. SEQUENCE Is a set of numbers written in order by the application of a definite rule.
- 5. SEQUENCE Example: 3, 5, 7, 9… +2 +2 +2 11 +2
- 6. SEQUENCE 3, 5, 7, 9… TERMS 1st term 2nd term 3rd term 4th term
- 7. Examples of Sequence: 3, 6, 9, 12… 1, 4, 9, 16… 2, 5, 8, 11 …
- 8. 3, 6, 9, 12… How to formulate the rule? What i s the nth Term Rule? What are the Next Three Terms?
- 9. 3, 6, 9, 12… 3, 6, 9, 12… How to formulate the Rule? 1st term 2nd term 3rd term 4th term 3 x 1 3 x 2 3 x 3 3 x 4 What is the nth Term Rule? 3n
- 10. What are the next three terms? 3, 6, 9, 12… nth Term Rule = 3n (3 x n) 3, 6, 9, 12, ____, _____, _____, 1st term 2nd term 3rd term 4th term 5th term 6th term 7th term = 3n = 3 x 5 = 15 15 = 3n = 3 x 6 = 18 18 = 3n = 3 x 7 = 21 21
- 11. What is 20th term in the sequence? 3, 6, 9, 12, 15, 18, 21… _______________ nth Term Rule = 3n = 3n = 3 x 20 = 60
- 12. 2, 5, 8, 11 … How to formulate the rule? What i s the nth Term Rule? What are the Next Three Terms?
- 13. 2, 5, 8, 11 … How to formulate the Rule? 2, 5, 8, 11 5 – 2 = 3 8 – 5 = 3 11 – 8 = 3
- 14. Guess: 3n + 1 2, 5, 8, 11 … 2, 5, 8, 11 5 – 2 = 3 8 – 5 = 3 11 – 8 = 3 Check: 3n + 1 = 3(1) + 1 = 3 + 1 = 4 What is the nth Term Rule?
- 15. Guess: 3n - 2 2, 5, 8, 11 … 2, 5, 8, 11 5 – 2 = 3 8 – 5 = 3 11 – 8 = 3 Check: 3n - 2 = 3(1) - 2 = 3 - 2 = 1 What is the nth Term Rule?
- 16. Guess: 3n - 1 2, 5, 8, 11 … 2, 5, 8, 11 5 – 2 = 3 8 – 5 = 3 11 – 8 = 3 Check: 3n - 1 = 3(1) - 1 = 3 - 1 = 2 What is the nth Term Rule? 3n- 1
- 17. What are the next three terms? 2, 5, 8, 11 … nth Term Rule = 3n-1 2, 5, 8, 11, ____, ____, _____ = 3n - 1 = 3 (5) - 1 = 15 - 1 = 14 14 = 3n - 1 = 3 (6) - 1 = 18 - 1 = 17 17 = 3n - 1 = 3 (7) - 1 = 21 - 1 = 20 20
- 18. What is the 50th term in sequence? 2, 5, 8, 11 … nth Term Rule = 3n-1 = 3n - 1 = 3 (50) - 1 = 150 - 1 = 149
- 19. How to formulate the rule? 1, 4, 9, 16… 1, 4, 9, 16… 4-1 +3 +5 +7 9-4 16-9 +9 25
- 20. How to formulate the rule? 1, 4, 9, 16… 1, 4, 9, 16… 1 X 1 2 X 2 3 X 3 4 X 4 What is the nth Term Rule? 𝒏𝟐
- 21. What are the next three terms in the sequence? 1, 4, 9, 16… nth term rule: 𝒏𝟐 1, 4, 9, 16, ___, ____, ____, 𝒏𝟐 𝟓𝟐 25 25 𝒏𝟐 𝟔𝟐 36 𝒏𝟐 𝟕𝟐 49 36 49
- 22. 1, 4, 9, 16… What is the 15th term in sequence? nth term rule: 𝒏𝟐 𝒏𝟐 𝟏𝟓𝟐 225 1, 4, 9, 16… 225
- 23. Direction: Write the rule to find the nth term of the given sequence. Supply the next three terms after. Sequence nth Term Rule Next Three Terms 1. 5, 9, 13, 17… 2. 3, 8, 13, 18… 3. 6, 12, 18, 24, 30… 4 6, 13, 20, 27… 5. 7,11,15,19, …