Chapter 7: Probability Lesson 5: Independent Events Mrs. Parziale.
Chapter 3: Linear Functions Lesson 7 & 8: Recursive and Explicit Formulas for Arithmetic Sequences...
-
Upload
trevor-dalton -
Category
Documents
-
view
238 -
download
0
Transcript of Chapter 3: Linear Functions Lesson 7 & 8: Recursive and Explicit Formulas for Arithmetic Sequences...
![Page 1: Chapter 3: Linear Functions Lesson 7 & 8: Recursive and Explicit Formulas for Arithmetic Sequences Mrs. Parziale.](https://reader036.fdocuments.us/reader036/viewer/2022081504/5697bf9f1a28abf838c94fe7/html5/thumbnails/1.jpg)
Chapter 3: Linear Functions
Lesson 7 & 8: Recursive and Explicit Formulas for Arithmetic Sequences
Mrs. Parziale
![Page 2: Chapter 3: Linear Functions Lesson 7 & 8: Recursive and Explicit Formulas for Arithmetic Sequences Mrs. Parziale.](https://reader036.fdocuments.us/reader036/viewer/2022081504/5697bf9f1a28abf838c94fe7/html5/thumbnails/2.jpg)
An arithmetic sequence is a sequence with a
increase or decrease also known as the __________________
In the sequence 1000, 4000, 7000, 10,000, 13,000….
The constant between the terms is _________
constant
difference 3000
constant difference.
![Page 3: Chapter 3: Linear Functions Lesson 7 & 8: Recursive and Explicit Formulas for Arithmetic Sequences Mrs. Parziale.](https://reader036.fdocuments.us/reader036/viewer/2022081504/5697bf9f1a28abf838c94fe7/html5/thumbnails/3.jpg)
A recursive formula for the sequence would be:
a1 = 1000an = a n-1 + for n > 23000
![Page 4: Chapter 3: Linear Functions Lesson 7 & 8: Recursive and Explicit Formulas for Arithmetic Sequences Mrs. Parziale.](https://reader036.fdocuments.us/reader036/viewer/2022081504/5697bf9f1a28abf838c94fe7/html5/thumbnails/4.jpg)
Graph the coordinates of the sequence:
Term Value Coordinate
1 1000 (1,1000)
2
3
4
5
n an-1 + 3000 ( )
How would you describe the graph of this sequence?
![Page 5: Chapter 3: Linear Functions Lesson 7 & 8: Recursive and Explicit Formulas for Arithmetic Sequences Mrs. Parziale.](https://reader036.fdocuments.us/reader036/viewer/2022081504/5697bf9f1a28abf838c94fe7/html5/thumbnails/5.jpg)
Find the rate of change between two of the points.
m = (y1 - y2) = = (x1 - x2)
What would this suggest about the slope of the line in the graph of a linear sequence?
![Page 6: Chapter 3: Linear Functions Lesson 7 & 8: Recursive and Explicit Formulas for Arithmetic Sequences Mrs. Parziale.](https://reader036.fdocuments.us/reader036/viewer/2022081504/5697bf9f1a28abf838c94fe7/html5/thumbnails/6.jpg)
Arithmetic Sequences are also known as:
linear sequences
![Page 7: Chapter 3: Linear Functions Lesson 7 & 8: Recursive and Explicit Formulas for Arithmetic Sequences Mrs. Parziale.](https://reader036.fdocuments.us/reader036/viewer/2022081504/5697bf9f1a28abf838c94fe7/html5/thumbnails/7.jpg)
A formula for an arithmetic sequence that allows you to find the nth term of the sequence by substituting in the expression. known values
Explicit FormulasExplicit Formulas
![Page 8: Chapter 3: Linear Functions Lesson 7 & 8: Recursive and Explicit Formulas for Arithmetic Sequences Mrs. Parziale.](https://reader036.fdocuments.us/reader036/viewer/2022081504/5697bf9f1a28abf838c94fe7/html5/thumbnails/8.jpg)
Using the fact that the arithmetic sequence 1000, 4000, 7000, 10000, …
is linear find the equation of the line by using thepoint slope formula:
Pick point (1, 1000) and the slope m that you calculated to write the equation.
What is x for the given situation?
What is y?
y - y1 = m (x- x1)
![Page 9: Chapter 3: Linear Functions Lesson 7 & 8: Recursive and Explicit Formulas for Arithmetic Sequences Mrs. Parziale.](https://reader036.fdocuments.us/reader036/viewer/2022081504/5697bf9f1a28abf838c94fe7/html5/thumbnails/9.jpg)
This becomes the explicit formula for finding any term in the sequence.
Theorem for the nth term of an Arithmetic Sequence:The nth term an of an arithmetic sequence with first term a1 and constant difference d is given by the explicit formula:
an = a1 + ( n - 1) d
![Page 10: Chapter 3: Linear Functions Lesson 7 & 8: Recursive and Explicit Formulas for Arithmetic Sequences Mrs. Parziale.](https://reader036.fdocuments.us/reader036/viewer/2022081504/5697bf9f1a28abf838c94fe7/html5/thumbnails/10.jpg)
Given the following arithmetic sequence: 100, 120, 140, 160,…
a) Define the sequence explicitly:
b) Find the 10th term.
ExampleExample
![Page 11: Chapter 3: Linear Functions Lesson 7 & 8: Recursive and Explicit Formulas for Arithmetic Sequences Mrs. Parziale.](https://reader036.fdocuments.us/reader036/viewer/2022081504/5697bf9f1a28abf838c94fe7/html5/thumbnails/11.jpg)
The first row of the theater has 15 seats in it. Each subsequent row has 3 more seats that the previous row. If the last row has 78 seats, how many rows are in the theater?
ExampleExample
![Page 12: Chapter 3: Linear Functions Lesson 7 & 8: Recursive and Explicit Formulas for Arithmetic Sequences Mrs. Parziale.](https://reader036.fdocuments.us/reader036/viewer/2022081504/5697bf9f1a28abf838c94fe7/html5/thumbnails/12.jpg)
Closure
• The increase or decrease in an arithmetic sequence is called a ________________.
• What is the general form of the recursive formula of an arithmetic sequence?
• What is the explicit formula nth Term of an Arithmetic Sequence?
• What are the a1, an, and d values?
• Given a sequence, how do you find the equation of the line that represents it.