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Name:________________________________________________________________________________Date:_____/_____/__________ BRAIN BLITZ/Warm-UP Quiz Day!! Identify the properties using the following answer bank: Commutative of Addition; Commutative of Multiplication; Associative of Addition; Associative of Multiplication; Identity of Addition; Identity of Multiplication; Inverse of Addition; Inverse of Multiplication; Zero Prop.; Distributive Property 1. 1 • 24 = 24 6. -35x + 35x = 0 2. 3(a + 4) = 3a + 3(4) 7. 0(8x) = 0 3. 4(xy) = (4x)y 8. 3/4 • 4/3 = 1 4. 9 + (ab) = (ab) + 9 9. 6(9y) = 9y(6) 5. 5xy + 0 = 5xy 10. (3 + 4x) + 2 = 3 + (4x + 2) Short Answer: Apply both the commutative and associative properties in order to re-write the following expression in a way that makes it easier to evaluate mentally. Then, give answer. _________________________________________________Answer: _______ Identify the properties that were used to simplify the following expression: 12. (5 + 7) Step 1: ___________________________________________________ Step 2: ___________________________________________________ Step 3: ( ) ___________________________________________________ Step 4: ___________________________________________________ Step 5: __________________________________________________
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The quotient of a number and 6 is the same as 6.
Fill-in the missing parts of the table by translating the following algebraic sentences: 13. 4 less than a number 14. 4 less a number 15. The quotient of a number and 6 is the same as 6. 16. twice a number, decreased by 12 17. twice the sum of a number and -2 18. The difference of 9 and a number is -10. 19. 2 more than the product of 15 and a number 20. A number squared is 4 less than 6.
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Today’s Lesson: What: sequences Why:
To identify the common difference or ratio in a sequence and determine whether or not the sequence is arithmetic, geometric, or neither.
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vocabulary: subtracting difference dividing ratio
Arithmetic Sequence— goes from one term to the next term by always adding or _________________________ the same value. We call this the common __________________________. Geometric Sequence— goes from one term to the next term by always multiplying or ______________________ by the same value. We call this the common _________________. subtracting difference dividing ratio
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Sequence Rule “plus eight” Diff: 8 27 Arithmetic n + 8 “times two”
Common Difference OR Ratio Arithmetic or Geometric? Variable Expression 1) -5, 3, 11, 19, ___ 2) 5, 10, 20, 40, ___ 3) 16, 10, 4, -2, ___ 4) 80, 20, 5, ___ 1, 2, 4, 7, 11, ___ “plus eight” Diff: 8 27 Arithmetic n + 8 “times two” Ratio: 2 80 Geometric 2n “minus six” Diff: -6 -8 Arithmetic n - 6 𝟓 𝟒 “divide by four” Ratio: 𝟏 𝟒 𝒏 𝟒 Geometric 16 NA NA Neither NA
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Sequence Rule “times three” Ratio: 3 Geometric 9 3n 4 NA NA Neither NA
Common Difference OR Ratio Arithmetic or Geometric? Variable Expression 𝟏 𝟗 , 𝟑 𝟗 , 1, 3, ___ 7) 1, 1, 2, 2, 3, 3, ___ Bonus: 1,1, 2, 3, 5, 8, 13, __ “times three” Ratio: 3 Geometric 9 3n 4 NA NA Neither NA NA NA Neither NA 21
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Which of the following sequences is an arithmetic sequence? 3, 9, 1, 3, 6, 10, 52, 49, 46, What would be the 5th term of the following geometric 1, 5, 125 625 30
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sequences is a geometric sequence? 27, 9, 3, 1 . . . 1, 2, 6, 24. . .
3) Which of the following sequences is a geometric sequence? 27, 9, 3, 1, 2, 6, 2, 4, 6, 4) What is the common difference in the following arithmetic sequence? 10, 6, 2, 4 -4 CV
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5) What is the common ratio in the following geometric sequence? 1, -2, 4, -8, -2 2 6) Which variable expression describes the relationship between any two consecutive terms in the following sequence? -1, 4, -16, 4n -4n ¼ n
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7) Which variable expression describes the relationship between any two consecutive terms in the following sequence? -12, -4, 4, 12, n – 8 8n n + 8 8) What is the common ratio in the following geometric sequence? 88, 44, 22, 11, 11/ 2 - ½
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END OF LESSON The next slides are student copies of the notes for this lesson. These notes were handed out in class and filled-in as the lesson progressed. NOTE: The last slide(s) in any lesson slideshow represent the homework assigned for that day.
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Math-7 NOTES DATE: ______/_______/_______ What: sequences Why: To identify the common difference or ratio in a sequence and determine whether or not the sequence is arithmetic, geometric, or neither. NAME: Arithmetic Sequence— goes from one term to the next term by always adding or _____________________ the same value. We call this the common __________________________. Geometric Sequence— goes from one term to the next term by always multiplying or __________________ by the same value. We call this the common _________________. Sequence (What comes next?) Rule Common Difference OR Ratio Arithmetic or Geometric? Variable Expression 1) , 3, 11, 19, ___ 2) 5, 10, 20, 40, ___ 3) , 10, 4, -2, ___ 4) , 20, 5, ___ 1, 2, 4, 7, 11, ___ 6) , , 1, 3, ___ 1, 1, 2, 2, 3, 3, ___ BONUS: 1, 1, 2, 3, 5, 8, 13, ___
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Multiple Choice: Which of the following sequences is an arithmetic sequence? 3, 9, 1, 3, 6, 10, 52, 49, 46, What would be the 5th term of the following geometric sequence? 1, 5, 125 625 30 3) Which of the following sequences is a geometric sequence? 27, 9, 3, 1, 2, 6, 2, 4, 6, What is the common difference in the following arithmetic sequence? 10, 6, 2, 4 -4 5) What is the common ratio in the following geometric sequence? 1, -2, 4, -8, -2 2 Which variable expression describes the relationship between any two consecutive terms in the following sequence? -1, 4, -16, 4n -4n ¼ n Which variable expression describes the relationship between any two consecutive terms in the following sequence? -12, -4, 4, 12, n – 8 8n n + 8 What is the common ratio in the following geometric sequence? 88, 44, 22, 11, 11/ - ½
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Math- 7 Homework “sequences”
NAME:__________________________________________________________________________________DATE: _____/_____/__________ Math- 7 Homework “sequences” For the following sequences, identify what comes next and write the variable expression: What is the 8th term in the following sequence? 3, 9, 27, 81, 243, What is the 6th term of the geometric sequence shown? 80, 40, What is the common difference of the arithmetic sequence shown? -5, -1, 3, What is the common ratio of the geometric sequence shown? 729, 243, 81, 27, Write a variable expression that can be used represent the relationship between two consecutive terms of the following sequence: 8, 12, 16, What is the missing tem in this sequence? 1, 5, 25, ____, 625, …. 6, 12, 18, 24,… _____ 1, 4, 16, 64, … _____ 72, 36, 18, 9,…_____ 62, 58, 54, 50…_____ 5) 0.2, 0.4, 0.8, 1.6,…_____ 6) 1, 3, 9, 27,…_____ 7) 0, 16, 32, 48, 64…._____ 8) 1.2, 2.3, 3.4, 4.5, ….____ 9) 33, 37, 41, 45…._____ 10) 128, 32, 8, 2, …._____ 11) 2 , -6, 18, -54,…_____ 58, 50, 42, 34 …______ 30 Variable Expression: n + 6 Variable Expression: ____________________ Variable Expression: ____________________ Variable Expression: ____________________ Variable Expression: ____________________ Variable Expression: ____________________ Variable Expression: ____________________ Variable Expression: ____________________ Variable Expression: ____________________ Variable Expression: ____________________ Variable Expression: ____________________ Variable Expression: ____________________
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continued . . . Match each sequence with the variable expression that describes the relationship between the consecutive terms of the sequence. 13. Which of the above problems are arithmetic sequences? _________________________ 14. Which of the above problems are geometric sequences? _________________________ 1. ____ 2, 4, 6, 8, 10, … A. n + 10 2. ____ 1, 3, 9, 27, 71 B. 1/3 n 3. ____ 45, 41, 37, 33, 29, …. C n 4. ____ 11, 21, 31, 41, 51, …. D. n + 5 5. ____ 10, 5, 2.5, 1.25, 0.625, …. E. n + 2 6. ____ 11, 3, -5, -13, -21, …. F n 7. ____ 100, 20, 4, 0.8, 0.16,….. G. n + (-2) 8. ____ 7, 10.5, , , , ….. H . n + (-4) 9. ____ 36, 12, 4, 1.333, …. I n 10. ____ -3, -6, -12, -24, -48, J n 11. ____ -80, -75, -70, -65, -60, …. K. n + (-8) 12. ____ 1, -1, -3, -5, …. L. 2n
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