1. DO NOW /20/2015
1. an= a1 + (n-1)(4) and a1=2 List the first 6 terms of the sequence. 2. Given: 4, 9, 14, 19… What is the rule that describes the nth term?

2. CC3 LT 3B Geometric & Arithmetic Sequences
1. I can write arithmetic and geometric sequences (both recursively and with an explicit formula) from a graph, a description of a relationship, or input/output pairs from a table.
2. I can use the sequences to model
situations and translate between the two forms.
----- Meeting Notes (11/14/14 11:52) -----
T: Posts Powerpoint on board
S: Analyze the LT and identify words/phrases that they don't know.

3. What Questions come to mind??
Approach Independently
Create 2 Plans that might work by communicating with partner
Need: Student and Teacher actions for this IBE
----- Meeting Notes (11/14/14 11:52) -----
T: Posts IBE and says

4. I. Geometric Sequence - Definition
Multiplying
I. Geometric Sequence - Definition
Common Ratio is the rate at which the sequence is changing. Same as Constant Rate
A Geometric Sequence is a sequence of numbers (n terms) where the difference between each term has a common ratio. a1, a1r, a1r2, a1r3, … an
a1= first term in a sequence
1st Term
2nd Term
3rd Term
4thTerm
nth Term
Thoughts do we need to add a thought bubble for exponents.
T: how many terms do you see?
T: What patterns did you notice?
T: what does the exponents mean?
----- Meeting Notes (12/2/14 15:45) -----
T: what would the nth term be?
Adding
How is this different from an Arithmetic Sequence?

5. I. Geometric Sequence - Equation
B. Explicit Form
Why N-1? r
F(x) = Starting Value (common ratio)
Where will the students interact with the slide? What questions should be asked?
n represents natural numbers so zero is not included
-because the starting value is the 1st term, NOT the zero term.
If you made a table, it would be the value when y=1.
We minus one, so we can have the value when y=0

6. DO NOW 10/21/2015
Determine whether each sequence is Arithmetic or Geometric. Then find the common difference/common ratio.
a) 5, 9, 13, b) 6, 24, 96….
c) 64, 32, 16, 8… d) 19, 14, 9, 4…

7. DO NOW 10/22/2015 Find the 25th term for each sequence.
a) 5, 9, 13, b) 6, 24, 96….
c) 64, 32, 16, 8… d) 19, 14, 9, 4…

8. What could the decimal represent?
I. Geometric Sequence - Example
Divide 2nd number
by 1st number:
C. The table shows the spread of the flu virus.
Number of people who get sick from the flu.
1 week
2 weeks
3 weeks
4 weeks
5 weeks 2 16
128
1024
8192
x x x8
What could the decimal represent?
Number of healthy people during flu season.
1 week
2 weeks
3 weeks
4 weeks
5 weeks
2,500
875
306.25
107.19
37.5
x x x0.35
What is the common ratio for both tables?
What will be the results on week 8?

9. I. Geometric Sequence - Example (Continued)
Use the Geometric Sequence Formula
More than 4 million people are going to be sick in 8 weeks
8th Term = 4,194,304
Only about 2 people will still be healthy after 8 weeks of spreading the flu.
8th Term = 1.6

10. Are you going to be affected?
Culver City Population = 39,428
California Population = million
United States Population = million
OH NO!!!!!

11. Recall & Reproductions
Goal Problems
Recall & Reproductions
Routine
Find the nth term of the sequence: 1. 3, 12, 48, 192… n=10 2. List the first 3 terms of the sequence.
The tuition fees for the first three years of a high school are given in the table below. How much will it be in 5 years?
Move 5: Action Plan / Improve; NCTM 1, 8(1st iteration)
Action on Feedback:
Answer is
1,)
2.) an=4+5(n-1)
Non-routine … applied problem or tiles… .

12. Goal Problems Routine DOK 2
You visit the Grand Canyon and drop a penny off the edge of a cliff. The distance the penny will fall is 16 feet the first second, 48 feet the next second, 80 feet the third second, and so on in an arithmetic sequence. What is the total distance the object will fall in 6 seconds?
Move 5: Action Plan / Improve; NCTM 1, 8(1st iteration)
Action on Feedback:
Answer is
1,)
2.) an=4+5(n-1)
Non-routine … applied problem or tiles… .

13. Goal Problems
Routine 2
Move 5: Action Plan / Improve; NCTM 1, 8(1st iteration)
Action on Feedback:
Answer is
1,)
2.) an=4+5(n-1)
Non-routine … applied problem or tiles… .

14. Goal Problems NON-Routine DOK 3
 You complain that the hot tub in your hotel suite is not hot enough. 
The hotel tells you that they will increase the temperature by 10% each hour.  If the current temperature of the hot tub is 75º F, what will be the temperature of the hot tub after 3 hours, to the nearest tenth of a degree?
Move 5: Action Plan / Improve; NCTM 1, 8(1st iteration)
Action on Feedback:
Answer is
1,)
2.) an=4+5(n-1)
Non-routine … applied problem or tiles… .

15. Goal Problems NON-Routine DOK 3
Move 5: Action Plan / Improve; NCTM 1, 8(1st iteration)
Action on Feedback:
Answer is
1,)
2.) an=4+5(n-1)
Non-routine … applied problem or tiles… .

16. Goal Problems 10/26/2015 NON-Routine DOK 3
 If you have a sequence starting with 5,15….. and some term 135 later in the sequence,
Could the sequence be arithmetic? If so, what is the equation of the nth term and what term is 135?
2. Could the sequence be geometric? If so, what is the equation of the nth term and what term is 135?
Move 5: Action Plan / Improve; NCTM 1, 8(1st iteration)
Action on Feedback:
Answer is
1,)
2.) an=4+5(n-1)
Non-routine … applied problem or tiles… .

17. I. Arithmetic Sequence - Definition
The value from one term to the next. Must be the same amount.
An Arithmetic Sequence is a sequence of numbers (n terms) where the difference between each term has a common difference.
a1, a1 + d, a1 + 2d, a1 + 3d, … n
a1= first term in a sequence
1st Term
2nd Term
3rd Term
4thTerm
nth Term
a1, a1 )+ d, a0 + 2d, a0 + 3d, … a0 + (n-1)d
Goal: By the end of the slide, students should have notes on what “a1, n and d are”
a0, a0 + d, a0 + 2d, a0 + 3d, … a0 + (n-1)d
Where n is the number of terms in the sequence
And a0 is the first term.
a1, a1 + d, a1 + 2d, a1 + 3d, … a1 + (n)d

18. I. Arithmetic Sequence - EquationB.
Explicit Form
The only thing that changes for each sequence is the a1 and the d
Definition: Straight forward way of finding an amount.
Why (n-1)
N is used to describe the terms in the sequence we are looking for.
Where will the students interact with the slide? What questions should be asked?
F(x) = Starting Value + Rate of Change (n-1)

19. C. Find a rule to describe the nth term of the following sequence.
I. Arithmetic Sequence - Example
C. Find a rule to describe the nth term of the following sequence.
Approach from Unit 1:
X is the figure number
Y is the number tiles.
Can I organize the details?
Use y = mx +b to find the rule
Approach : Can I use a table? Can organize it a different way?
Identify first term? Pattern? identify common difference? …. Should we use Explicit or Recursive term?
Plan1: 1.) organize data 2.) use terms to find(first common difference plug into explicit
Plan2:1.) organize data 2.) graph or find equation from table.
Execute:
Plan: X 1 2 3 Y 5 9 13
- 4
+ 4
+ 4

20. Plan from Unit 1 y = 4 x + 1 The rule for the nth term is y = 4n+1
C. Find a rule to describe the nth term of the following sequence.
Plan: X 1 2 3 Y 5 9 13
- 4
+ 4
+ 4
Y-intercept
Rate of change
Rate of change
Execute:
y = mx + b
y = 4 x + 1
The rule for the nth term is y = 4n+1
Approach : Can I use a table? Can organize it a different way?
Identify first term? Pattern? identify common difference? …. Should we use Explicit or Recursive term?
Plan1: 1.) organize data 2.) use terms to find(first common difference plug into explicit
Plan2:1.) organize data 2.) graph or find equation from table.
Execute:
Y-intercept is the number of tiles when x =0

21. Plan from Unit 2
C. Find a rule to describe the nth term of the following sequence.
Approach:
What kind of pattern?
Adds 4 each time
Arithmetic Sequence
Re-write pattern as 5, 9, 13, 17
Plan :
Use Sequence Equation
Need to find parts of equation
a1 , d, n, an
Approach : Can I use a table? Can organize it a different way?
Identify first term? Pattern? identify common difference? …. Should we use Explicit or Recursive term?
Plan1: 1.) organize data 2.) use terms to find(first common difference plug into explicit
Plan2:1.) organize data 2.) graph or find equation from table.
Execute:
Common Difference
What gets added each time
First term

22. C. Find a rule to describe the nth term of the following sequence.
Plan from Unit 2
C. Find a rule to describe the nth term of the following sequence.
Execute:
Equation an= a1+ d(n-1)
a1 = the first term d = the common difference
a1= , , 13+4, 17
d= 4
The rule for the nth term is an = (n-1)
Approach : Can I use a table? Can organize it a different way?
Identify first term? Pattern? identify common difference? …. Should we use Explicit or Recursive term?
Plan1: 1.) organize data 2.) use terms to find(first common difference plug into explicit
Plan2:1.) organize data 2.) graph or find equation from table.
Execute:

23. C. Find a rule to describe the nth term of the following sequence.
I. Arithmetic and Geometric Sequence
C. Find a rule to describe the nth term of the following sequence.
Solution from Unit 1
y= 4n +1
Solution from Unit 2
an= 5 + 4(n-1)
Approach : Can I use a table? Can organize it a different way?
Identify first term? Pattern? identify common difference? …. Should we use Explicit or Recursive term?
Plan1: 1.) organize data 2.) use terms to find(first common difference plug into explicit
Plan2:1.) organize data 2.) graph or find equation from table.
Execute:
Are they the same? Why or why not?

24. Recall & Reproductions
Goal Problems (LT 2D #1)
Recall & Reproductions
Routine
Given: an= a1 + 3 (n-1) and a1=2 List the first 6 terms of the sequence.
Given: 4, 9, 14, 19… What is the rule that describes the nth term?
Move 5: Action Plan / Improve; NCTM 1, 8(1st iteration)
Action on Feedback:
Answer is
1,)
2.) an=4+5(n-1)
Non-routine … applied problem or tiles… .

25. Active Practice (LT 2D #1)
Recall & Reproductions
Routine
Insert Recall Practice here
Insert Routine Practice Here
Move 5: Action Plan / Improve; NCTM 1, 8(1st iteration)
Action on Feedback:
Answer is
1,)
2.) an=4+5(n-1)
Non-routine … applied problem or tiles… .

26. I. Arithmetic and Geometric Sequence
E. Connections
Sequences
Arithmetic
Ex.
Explicit
Recursive
Geometric Ex
Carol what do you think? Where would the equations go? .. I left places for students to add example problems. Thoughts?