1. 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: __________________________________________________

2. 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.

3. 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.

4. 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

5. 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

6. 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

7. 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

8. 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

9. 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

10. 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

11. 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.

12. 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, ___

13. 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

14. 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: ____________________

15. 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