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# AA 1.7

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• ### AA 1.7

1. 1. Warm Up
2. 2. Warm Up 1. Find the next three terms of the sequence: 81, 27, 9, 3,__, __, __
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. 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. 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. 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. 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. 8. 1.7 Explicit Formulas for Sequences
9. 9. 1.7 Explicit Formulas for Sequences E. Q. - How do we evaluate sequences?
10. 10. Vocabulary
11. 11. Vocabulary • TERM - each number in a sequence
12. 12. Vocabulary • TERM - each number in a sequence • SEQUENCE - function whose domain is the set of natural numbers from 1 to n
13. 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. 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. 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. 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. 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. 18. Examples
19. 19. Examples 1. Use n(n + 1) to ﬁnd the ﬁfteenth rectangular number. €
20. 20. Examples 1. Use n(n + 1) to ﬁnd the ﬁfteenth rectangular number. 15(15 + 1) €
21. 21. Examples 1. Use n(n + 1) to ﬁnd the ﬁfteenth rectangular number. 15(15 + 1) € 15(16)
22. 22. Examples 1. Use n(n + 1) to ﬁnd the ﬁfteenth rectangular number. 15(15 + 1) € 15(16) 240
23. 23. Examples 1. Use n(n + 1) to ﬁnd the ﬁfteenth rectangular number. 15(15 + 1) € 15(16) 240 SEQUENCE NOTATION:
24. 24. Examples 1. Use n(n + 1) to ﬁnd the ﬁfteenth rectangular number. 15(15 + 1) € 15(16) 240 SEQUENCE NOTATION: t20 = 440
25. 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. 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. 27. 2. Consider the formula t n = 15 + 2(n −1) for integers n ≥ 1. €
28. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 42. LAST ONE!!!
43. 43. LAST ONE!!! Consider the sequence t, squares of consecutive positive integers.
44. 44. LAST ONE!!! Consider the sequence t, squares of consecutive positive integers. a. Give an explicit formula for the sequence.
45. 45. LAST ONE!!! Consider the sequence t, squares of consecutive positive integers. a. Give an explicit formula for the sequence. 2 tn = n €
46. 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. 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. 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. 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. 50. Homework Page 46 & 47 10 - 28