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![Formula:
𝑛
𝑆𝑛 =
2
(𝑎1 + 𝑎𝑛)
𝑛
𝑆𝑛 =
2
[2𝑎1 + 𝑛− 1 𝑑]
𝑎𝑛 = 𝑎1 + 𝑛− 1 𝑑](https://image.slidesharecdn.com/math10aug-230912222027-ca365d46/85/math-10-aug-6-2023-pptx-29-320.jpg)
![Using the formula:
𝑛
𝑆𝑛 =
2
[2𝑎1 + 𝑛− 1 𝑑
]
10
𝑆10 =
2
[2(5) + 10 − 1 4]
d = 9 -
5
𝑆10 = 5 10 + 9 4 = 5 46 = 𝟐𝟑𝟎](https://image.slidesharecdn.com/math10aug-230912222027-ca365d46/85/math-10-aug-6-2023-pptx-31-320.jpg)
![Formula:
𝑛
𝑆𝑛 =
2
(𝑎1 + 𝑎𝑛)
𝑛
𝑆𝑛 =
2
[2𝑎1 + 𝑛− 1 𝑑]
𝑎𝑛 = 𝑎1 + 𝑛− 1 𝑑](https://image.slidesharecdn.com/math10aug-230912222027-ca365d46/75/math-10-aug-6-2023-pptx-29-2048.jpg)
![Using the formula:
𝑛
𝑆𝑛 =
2
[2𝑎1 + 𝑛− 1 𝑑
]
10
𝑆10 =
2
[2(5) + 10 − 1 4]
d = 9 -
5
𝑆10 = 5 10 + 9 4 = 5 46 = 𝟐𝟑𝟎](https://image.slidesharecdn.com/math10aug-230912222027-ca365d46/75/math-10-aug-6-2023-pptx-31-2048.jpg)
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math 10 aug. 6, 2023.pptx
- 2. A sequence isa function whose domain is the finite set {1,23, …, n} or the infinite set {1,2 ,3,…}.
- 3. 2 3 45 Example: n 1 a(n) 4 5 6 7
- 4. 2 3 4… Example: n1 a(n) 2 4 6 8…
- 5. Activity: Termafter Term Findthe first five terms of the sequence given the nth term.
- 6. 1. 𝑎𝑛= 𝑛+4 2. 𝑎𝑛= 2𝑛− 1 3. 𝑎𝑛= 12 − 3𝑛 4. 𝑎𝑛= 3𝑛 5. 𝑎𝑛= (−2)𝑛
- 7. Activity: Getting toknow you! What is the nth term for each sequence below?
- 8. 1. 3, 5,7, 9, 11, … 2. 3, 4, 5, 6, 7, … 3. 6, 8, 10, 12, 15, … 4. 15, 17, 19, 21, 23, ... 5. 11, 14, 17, 20, 23, ...
- 9.
- 10. An arithmetic sequence isa sequence where every term after the first is obtained by adding a constant called the common difference.
- 11. The sequences 1,4,7,10,... and15, 11, 7, 3,... are examples of arithmetic sequences since each one has a common difference of 3 and -4.
- 12. Arithmetic Rule an= a1+(n- 1)d •a1 is the first term in the sequence •n is the number of the term you are trying to determine •d is the common difference •an is the value of the term that are looking for
- 13. Try this… Use thearithmetic formula to determine the 100th term of the following sequence: 75, 25, -25, -75, -125,…
- 14. an = a1+(n - 1)d = 75 + (100 – 1)(-50) = -4875 a1 = 75 n = 100 d = -50
- 15. Try this… Use thearithmetic formula to determine the 10th term of the following sequence: 5, 12, 19, 26,…
- 16. an = a1+(n - 1)d = 5 + (10 – 1)(7) = 68 a1 = 5 n = 10 d = 7
- 17. What is missing? 1.3, 12, 21, 30 , 39 , 48 2. 8, 3, -2, -7 ,-12 3. 5, 12, 19 ,
- 18. What is missing? 4.-4 , 0 , 4 , 8 , 12 , 16 5. -1, 7 , 15 , 23, 31, 39 6. 13, 7 , 1 ,_-5_,-11.-
- 19. Insert three terms between2 and 34 of an arithmetic sequence.
- 20. ARITHMETIC MEANS The termsbetween any two consecutive terms of an arithmetic sequence.
- 21. Insert4 arithmetic means between5 and 25.
- 22. Solution: Since we arerequired to insert 4terms, then there will be 6 terms in all.
- 23. Let 𝑎1 =5and 𝑎6 = 25 5, 𝑎2,𝑎3,𝑎4,𝑎5,25
- 24. 5, 𝑎2,𝑎3,𝑎4,𝑎5,25 Let 𝑎6= 𝑎1+ 25 = 5 + 6 − 1 𝑑 5 𝑑 20 − 5 = 5𝑑 4 = 𝑑
- 25. 5, 𝑎2,𝑎3,𝑎4,𝑎5,25 𝑎2 =𝑎1+ (1)(𝑑) n = 2 (2 – 1) = 1 𝑎2 = 5 + 1 4 = 9 𝑎3 = 5 + (2)(4)=13 𝑎4 = 5 + 3 𝑎5 = 5 + 4 = 17 4 4 = 21
- 26. Insert 2 arithmetic meansbetween ½ and 2.
- 27. ARITHMETIC SUM Sum ofthe terms in an arithmetic sequence.
- 28. What is 1 +2 + 3 + …+ 50 + 51 +… + 98 + 99 +100?
- 29. Formula: 𝑛 𝑆𝑛 = 2 (𝑎1 +𝑎𝑛) 𝑛 𝑆𝑛 = 2 [2𝑎1 + 𝑛− 1 𝑑] 𝑎𝑛 = 𝑎1 + 𝑛− 1 𝑑
- 30. Example: Find the sumof the first 10 terms of the arithmetic sequence 5, 9, 13, 17,…
- 31. Using the formula: 𝑛 𝑆𝑛= 2 [2𝑎1 + 𝑛− 1 𝑑 ] 10 𝑆10 = 2 [2(5) + 10 − 1 4] d = 9 - 5 𝑆10 = 5 10 + 9 4 = 5 46 = 𝟐𝟑𝟎
- 32. Example: Find the sumof the first 20 terms of the arithmetic sequence -2, -5, -8, -11, … -610
- 33. Activity: How well do youknow me?
- 34. Which of thefollowing sequences is an arithmetic sequence? Why?
- 35. 1. 3, 7,11, 15, 19 2. 4, 16, 64, 256 3. 48, 24, 12, 6, 3, … 4. 1, 4, 9, 16, 25, 36 5. 1, ½ , 0, - ½
- 36. 6. – 2,4, - 8, 16, … 7. 1, 0, -1, -2, -3 8. ½ , 1/3, ¼ , 1/5 9. 3x, x, x/3, x/9 10. 9.5, 7.5, 5.5, 3.5
- 37. Find the 25thterm of the arithmetic sequence 3, 7, 11, 15, 19,…
- 38. The second termof the arithmetic sequence is 24 and the fifth term is 3. Find the first term and the common difference
- 39. Give the arithmetic sequenceof 5 terms if the first term is 8 and the last term is 100.
- 40. What must bethe value of k so that 5k – 3, k +2, and 3k – 11 will form an arithmetic sequence?