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  • 1. Warm Up
  • 2. Warm Up 1. Find the next three terms of the sequence: 81, 27, 9, 3,__, __, __
  • 3. Warm Up 1. Find the next three terms of the sequence: 81, 27, 9, 3,__, __, __ 2. Evaluate 4n - 6, when n =14.
  • 4. Warm Up 1. Find the next three terms of the sequence: 81, 27, 9, 3,__, __, __ Divide the previous term by 3 to get 1, 1/3, 1/9 2. Evaluate 4n - 6, when n =14.
  • 5. Warm Up 1. Find the next three terms of the sequence: 81, 27, 9, 3,__, __, __ Divide the previous term by 3 to get 1, 1/3, 1/9 2. Evaluate 4n - 6, when n =14. 4(14) - 6
  • 6. Warm Up 1. Find the next three terms of the sequence: 81, 27, 9, 3,__, __, __ Divide the previous term by 3 to get 1, 1/3, 1/9 2. Evaluate 4n - 6, when n =14. 4(14) - 6 56 - 6
  • 7. Warm Up 1. Find the next three terms of the sequence: 81, 27, 9, 3,__, __, __ Divide the previous term by 3 to get 1, 1/3, 1/9 2. Evaluate 4n - 6, when n =14. 4(14) - 6 56 - 6 50
  • 8. 1.7 Explicit Formulas for Sequences
  • 9. 1.7 Explicit Formulas for Sequences E. Q. - How do we evaluate sequences?
  • 10. Vocabulary
  • 11. Vocabulary • TERM - each number in a sequence
  • 12. Vocabulary • TERM - each number in a sequence • SEQUENCE - function whose domain is the set of natural numbers from 1 to n
  • 13. Vocabulary • TERM - each number in a sequence • SEQUENCE - function whose domain is the set of natural numbers from 1 to n • SUBSCRIPT - number or variable that is written below and to the right of another, also called the index
  • 14. Vocabulary • TERM - each number in a sequence • SEQUENCE - function whose domain is the set of natural numbers from 1 to n • SUBSCRIPT - number or variable that is written below and to the right of another, also called the index • EXPLICIT FORMULA for the nth term -
  • 15. Vocabulary • TERM - each number in a sequence • SEQUENCE - function whose domain is the set of natural numbers from 1 to n • SUBSCRIPT - number or variable that is written below and to the right of another, also called the index • EXPLICIT FORMULA for the nth term - • use it to calculate the nth term
  • 16. Vocabulary • TERM - each number in a sequence • SEQUENCE - function whose domain is the set of natural numbers from 1 to n • SUBSCRIPT - number or variable that is written below and to the right of another, also called the index • EXPLICIT FORMULA for the nth term - • use it to calculate the nth term • can calculate any term in the sequence
  • 17. Vocabulary • TERM - each number in a sequence • SEQUENCE - function whose domain is the set of natural numbers from 1 to n • SUBSCRIPT - number or variable that is written below and to the right of another, also called the index • EXPLICIT FORMULA for the nth term - n(n + 1) 2 • use it to calculate the nth term • can calculate any term in the sequence €
  • 18. Examples
  • 19. Examples 1. Use n(n + 1) to find the fifteenth rectangular number. €
  • 20. Examples 1. Use n(n + 1) to find the fifteenth rectangular number. 15(15 + 1) €
  • 21. Examples 1. Use n(n + 1) to find the fifteenth rectangular number. 15(15 + 1) € 15(16)
  • 22. Examples 1. Use n(n + 1) to find the fifteenth rectangular number. 15(15 + 1) € 15(16) 240
  • 23. Examples 1. Use n(n + 1) to find the fifteenth rectangular number. 15(15 + 1) € 15(16) 240 SEQUENCE NOTATION:
  • 24. Examples 1. Use n(n + 1) to find the fifteenth rectangular number. 15(15 + 1) € 15(16) 240 SEQUENCE NOTATION: t20 = 440
  • 25. Examples 1. Use n(n + 1) to find the fifteenth rectangular number. 15(15 + 1) € 15(16) 240 SEQUENCE NOTATION: t20 = 440 “t sub 20”
  • 26. Examples 1. Use n(n + 1) to find the fifteenth rectangular number. 15(15 + 1) € 15(16) 240 SEQUENCE NOTATION: t20 = 440 “t sub 20” means the 20th term is 440
  • 27. 2. Consider the formula t n = 15 + 2(n −1) for integers n ≥ 1. €
  • 28. 2. Consider the formula tn = 15 + 2(n −1) for integers n ≥ 1. a. what are the first four terms generated by it? €
  • 29. 2. Consider the formula tn = 15 + 2(n −1) for integers n ≥ 1. a. what are the first four terms generated by it? 15 + 2(1-1) € ->
  • 30. 2. Consider the formula tn = 15 + 2(n −1) for integers n ≥ 1. a. what are the first four terms generated by it? 15 + 2(1-1) € -> 15 + 2(0) ->
  • 31. 2. Consider the formula tn = 15 + 2(n −1) for integers n ≥ 1. a. what are the first four terms generated by it? 15 + 2(1-1) € -> 15 + 2(0) -> 15 + 0 = 15
  • 32. 2. Consider the formula tn = 15 + 2(n −1) for integers n ≥ 1. a. what are the first four terms generated by it? 15 + 2(1-1) € -> 15 + 2(0) -> 15 + 0 = 15 VOLUNTEERS FOR THE NEXT THREE???
  • 33. 2. Consider the formula tn = 15 + 2(n −1) for integers n ≥ 1. a. what are the first four terms generated by it? 15 + 2(1-1) € -> 15 + 2(0) -> 15 + 0 = 15 VOLUNTEERS FOR THE NEXT THREE??? 2. b. Find t 8 . €
  • 34. 2. Consider the formula tn = 15 + 2(n −1) for integers n ≥ 1. a. what are the first four terms generated by it? 15 + 2(1-1) € -> 15 + 2(0) -> 15 + 0 = 15 VOLUNTEERS FOR THE NEXT THREE??? 2. b. Find t 8 . 15 + 2 (8 -1 ) €
  • 35. 2. Consider the formula tn = 15 + 2(n −1) for integers n ≥ 1. a. what are the first four terms generated by it? 15 + 2(1-1) € -> 15 + 2(0) -> 15 + 0 = 15 VOLUNTEERS FOR THE NEXT THREE??? 2. b. Find t 8 . 15 + 2 (8 -1 ) 15 + 2(7) €
  • 36. 2. Consider the formula tn = 15 + 2(n −1) for integers n ≥ 1. a. what are the first four terms generated by it? 15 + 2(1-1) € -> 15 + 2(0) -> 15 + 0 = 15 VOLUNTEERS FOR THE NEXT THREE??? 2. b. Find t 8 . 15 + 2 (8 -1 ) 15 + 2(7) 15 + 14 €
  • 37. 2. Consider the formula tn = 15 + 2(n −1) for integers n ≥ 1. a. what are the first four terms generated by it? 15 + 2(1-1) € -> 15 + 2(0) -> 15 + 0 = 15 VOLUNTEERS FOR THE NEXT THREE??? 2. b. Find t 8 . 15 + 2 (8 -1 ) 15 + 2(7) 15 + 14 29 €
  • 38. 3. Suppose you drop a ball from the top of a 50 foot wall. On each bounce the ball rises to 75% of the previous height. The heights form a sequence.
  • 39. 3. Suppose you drop a ball from the top of a 50 foot wall. On each bounce the ball rises to 75% of the previous height. The heights form a sequence. What are the first three bounce heights and after how many bounces does the ball rise < 10 feet? YOU TRY!!!
  • 40. 3. Suppose you drop a ball from the top of a 50 foot wall. On each bounce the ball rises to 75% of the previous height. The heights form a sequence. What are the first three bounce heights and after how many bounces does the ball rise < 10 feet? YOU TRY!!! HINT: take .75 times the previous height to get the new one
  • 41. 3. Suppose you drop a ball from the top of a 50 foot wall. On each bounce the ball rises to 75% of the previous height. The heights form a sequence. What are the first three bounce heights and after how many bounces does the ball rise < 10 feet? YOU TRY!!! HINT: take .75 times the previous height to get the new one 37.5 ft, 28.125 ft, 21.09375 ft and 6 bounces!
  • 42. LAST ONE!!!
  • 43. LAST ONE!!! Consider the sequence t, squares of consecutive positive integers.
  • 44. LAST ONE!!! Consider the sequence t, squares of consecutive positive integers. a. Give an explicit formula for the sequence.
  • 45. LAST ONE!!! Consider the sequence t, squares of consecutive positive integers. a. Give an explicit formula for the sequence. 2 tn = n €
  • 46. LAST ONE!!! Consider the sequence t, squares of consecutive positive integers. a. Give an explicit formula for the sequence. 2 tn = n b. What is the value of t sub 4? €
  • 47. LAST ONE!!! Consider the sequence t, squares of consecutive positive integers. a. Give an explicit formula for the sequence. 2 tn = n b. What is the value of t sub 4? € 1, 4, 9, 16
  • 48. LAST ONE!!! Consider the sequence t, squares of consecutive positive integers. a. Give an explicit formula for the sequence. 2 tn = n b. What is the value of t sub 4? € 1, 4, 9, 16 c. What is the value of t 250 ? €
  • 49. LAST ONE!!! Consider the sequence t, squares of consecutive positive integers. a. Give an explicit formula for the sequence. 2 tn = n b. What is the value of t sub 4? € 1, 4, 9, 16 c. What is the value of t 250 ? 2 250 = 62,500 € €
  • 50. Homework Page 46 & 47 10 - 28