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: 11. 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. 105 + 2 + 45 + 10 _________________________________________________Answer: _______ Identify the properties that were used to simplify the following expression: 12. -14 + 2(5 + 7) Step 1: -14 + 10 + 14 . . . . . ___________________________________________________ Step 2: -14 + 14 + 10. . . . . . ___________________________________________________ Step 3: (-14 + 14) + 10. . . . ___________________________________________________ Step 4: 0 + 10 . . . . . . . . . . . . ___________________________________________________ Step 5: 10 . . . . . . . . . . . . . . . . __________________________________________________

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.

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.

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

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

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

Which of the following sequences is an arithmetic sequence? 3, 9, 27 . . . 1, 3, 6, 10, 15 . . . 52, 49, 46, 43 . . . What would be the 5th term of the following geometric 1, 5, 25 . . . 125 625 30

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 . . . 1, 2, 6, 24. . . 2, 4, 6, 8 . . . 4) What is the common difference in the following arithmetic sequence? 10, 6, 2, -2 . . . 4 -4 ¼ CV

5) What is the common ratio in the following geometric sequence? 1, -2, 4, -8, 16 . . . -2 2 ½ 6) Which variable expression describes the relationship between any two consecutive terms in the following sequence? -1, 4, -16, 64 . . . 4n -4n ¼ n

7) Which variable expression describes the relationship between any two consecutive terms in the following sequence? -12, -4, 4, 12, 20 . . . n – 8 8n n + 8 8) What is the common ratio in the following geometric sequence? 88, 44, 22, 11, 11/2 . . . 2 ½ - ½

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.

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) -5, 3, 11, 19, ___ 2) 5, 10, 20, 40, ___ 3) 16, 10, 4, -2, ___ 4) 80, 20, 5, ___ 1, 2, 4, 7, 11, ___ 6) 1 9 , 3 9 , 1, 3, ___ 1, 1, 2, 2, 3, 3, ___ BONUS: 1, 1, 2, 3, 5, 8, 13, ___

Multiple Choice: Which of the following sequences is an arithmetic sequence? 3, 9, 27 . . . 1, 3, 6, 10, 15 . . . 52, 49, 46, 43 . . . What would be the 5th term of the following geometric sequence? 1, 5, 25 . . . 125 625 30 3) Which of the following sequences is a geometric sequence? 27, 9, 3, 1 . . . 1, 2, 6, 24. . . 2, 4, 6, 8 . . . What is the common difference in the following arithmetic sequence? 10, 6, 2, -2 . . . 4 -4 ¼ 5) What is the common ratio in the following geometric sequence? 1, -2, 4, -8, 16 . . . -2 2 ½ Which variable expression describes the relationship between any two consecutive terms in the following sequence? -1, 4, -16, 64 . . . 4n -4n ¼ n Which variable expression describes the relationship between any two consecutive terms in the following sequence? -12, -4, 4, 12, 20 . . . n – 8 8n n + 8 What is the common ratio in the following geometric sequence? 88, 44, 22, 11, 11/2 . . . - ½

Math- 7 Homework “sequences” NAME:__________________________________________________________________________________DATE: _____/_____/__________ Math- 7 Homework “sequences” For the following sequences, identify what comes next and write the variable expression: 13. What is the 8th term in the following sequence? 3, 9, 27, 81, 243, 729 . . . 14. What is the 6th term of the geometric sequence shown? 80, 40, 20 . . . 15. What is the common difference of the arithmetic sequence shown? -5, -1, 3, 7 . . . 16. What is the common ratio of the geometric sequence shown? 729, 243, 81, 27, 9 . . . Write a variable expression that can be used represent the relationship between two consecutive terms of the following sequence: 8, 12, 16, 20 . . . 18. 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: ____________________

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. 0.2n 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. 0.5n 7. ____ 100, 20, 4, 0.8, 0.16,….. G. n + (-2) 8. ____ 7, 10.5, 15.75, 23.625, 35.4375, ….. H . n + (-4) 9. ____ 36, 12, 4, 1.333, …. I. 1.5n 10. ____ -3, -6, -12, -24, -48, J. 3n 11. ____ -80, -75, -70, -65, -60, …. K. n + (-8) 12. ____ 1, -1, -3, -5, …. L. 2n