1. Lesson 4.6 Review: 4.1 - Writing Equations in Slope-Intercept Form
4.2 -
Writing Equations in Point-Slope Form
4.3 -
Writing Equations of Parallel & Perpendicular lines
4.4 -
Scatter Plots and Lines of Fit
4.5 -
Analyzing Lines of Fit

2. What are the next two images in this sequence?
Lesson 4.6
Arithmetic Sequences
What are the next two images in this sequence?
6 = 7* & 7=8*
What are the tenth image in this sequence?
10 = 11*
What are the thousandth image in this sequence?
1000 =10001 *

3. Objective
To Write Arithmetic Sequences, Graph Arithmetic Sequences and writing Function of Arithmetic Sequences.
Sequence:
An ordered list of numbers. Each number in the sequence is called a TERM. Each TERM (an) has a specific position in the sequence position “n” in the sequence.
Term 1 Term 2 Term 3 Term Term 10 nthterm
… an...
Pos. 1 Pos. 2 Pos. 3 Pos Pos. 10 nth Pos.

4. The difference between each pair of consecutive terms is the same.
Arithmetic Sequence:
The difference between each pair of consecutive terms is the same.
Term 1 Term 2 Term 3 Term Term 10 nthterm
… an...
Common Difference
Common Difference:
Each term is found by adding the common difference to the previous term

5. How do you extend an Arithmetic Sequence?
Example 1:
Write the next three terms of the arithmetic sequence:
-7, -14, -21, -28…
create a table to find the pattern.
Position
Term 1 2 3 4
Position
Term 1 2 3 4 5 6 7 -7
-14
-21
-28 -7
-14
-21
-28
-35
-42
-49
+(-7)
+(-7)
+(-7)
+(-7)
+(-7)
+(-7)
Write a left column question

6. Graphing an arithmetic sequence: 4,8,12,16
EQ #2 How do you graph arithmetic sequence and how do you identify arithmetic sequences from a graph
Example 2:
Graphing an arithmetic sequence: 4,8,12,16
graph the ordered pairs.
Position n
Term an 1 2 3 4 4 8 12 16 20
What is the common difference? 16 +4 12
What would be the next term? 8 20 4 2 4 6 8

7. EQ #2 (continued) Example 3:
Identifying an arithmetic sequence from a graph 20
create a table from the ordered pairs on the graph.
(1,15) 16
(2,12) 12
(3,9)
Position n
Term an 1 2 3 4 8
(4,6) 15 12 9 6 4
+(-3)
+(-3)
+(-3) 2 4 6 8
What is the common difference?
What would be the next term?
+(-3) 3
Write a left column question

8. Term (an) & difference (d)
EQ #3
How do you write an arithmetic sequence as a function?
Writing Arithmetic Sequences as Functions
Because consecutive terms of an arithmetic sequences have a common difference, the sequence has a constant rate of change. n an 1 4 2 8 3 12 16
nth
Position n
Term an
Term (an) & difference (d)
Numbers 1 2 3 4 :
nth term
1st or a1
2nd or a2
3rd or a3
4th or a4 :
nth term or an a1
a2 + d
a3 +2 d
a4 +3 d :
an +(n-1) d
4+(1-1)4 = 4
4 +(2-1)4 = 8
4+(3-1)4=12
4+(4-1)4=16 :
4+(n-1)(4) =an

9. an = a1 + ( n – 1 ) d EQ #3 (continued) an = a1 + ( n – 1 ) d
Writing Arithmetic Sequences as Functions (continued)
Since an is also the nth term in an arithmetic sequence with the first term a1 and a continuous difference “d” an equation for an arithmetic sequence can be written as:
an = a1 + ( n – 1 ) d n an 1 4 2 8 3 12
nth
an = a1 + ( n – 1 ) d
4 = 4 + ( (1) – 1 ) (4)
8 = 4 + ( (2) – 1 ) (4)
12 = 4 + ( (3) – 1 ) (4)

10. EQ #3 (continued) Example 4:
Write a function for the nth term for the arithmetic sequence : 5,9,14,19
Create a table
Position n
Term an 1 2 3 4 4 9 14 19 +5
(d)
What is the common difference?
What is the first term? 4
(a1)
Substitute difference and term for (a1) and (d)
an = 4 + ( n – 1 ) 5
an = 4 + 5n – 5
an = n

11. EQ #3 (continued) Example 5: Writing a real-life function
Online bidding for Sun Devil season tickets increases by $25 for each bid after an initial bid of $65
A. Write a function that represents this arithmetic sequence
Bid (n)
Amount (an) 1 2 3 4 65 90
115
140
an = 65 + ( n – 1 ) 25
an = n – 25
an = n

12. EQ #3 (continued) Example 5 (cont.): Writing a real-life function
Online bidding for Sun Devil season tickets increases by $25 for each bid after an initial bid of $65
B. Graph the arithmetic sequence.
250
200
Bid (n)
Amount (an) 1 2 3 4
150 65 90
115
140
100
C. The winning bid is $215. How many bids were there? 50
f(215) = n ...
7 = n 2 4 6 8
Write a summary of the lesson