1. Warm up:

2. Module 1 Arithmetic and Geometric Sequences

3. Essential Question: How can we use mathematical representations to model a pattern?

4. Essential Question: How can we use mathematical representations to model a pattern?
What does this mean?
Representation: A mathematical way to show a relationship such as a (table, graph, equation, diagram, or story context) – these are all mathematical models.
Example: Last class I chose to represent the checkerboard data with a table. Then I made an equation.
I could also make a graph.
𝑦=4𝑥+8
Size of white square
Number of colored tiles
1x1 12
2x2 16
3x3 20
4x4 24
5x5 25

8. Is the given sequence arithmetic?
Arithmetic Sequences
LESSON 11-2
Additional Examples
Is the given sequence arithmetic?
a. 7, 10, 13, 16, . . .
b. The sequence of dots in the “triangles” shown below.

9. Warm Up

10. Essential Question: How can we use mathematical representations to model a pattern?
What does this mean?
Representation: A mathematical way to show a relationship such as a (table, graph, equation, diagram, or story context) – these are all mathematical models.
Example: Last class I chose to represent the checkerboard data with a table.

11. 𝑑 𝑡 =4𝑡+1

12. Arithmetic Sequence Formulas
Recursive Formula
𝒇 𝟏 = _________
𝒇 𝒙 =𝒇 𝒙−𝟏 +𝒅
𝒇 𝟏 𝒊𝒔 𝒇𝒊𝒓𝒔𝒕 𝒕𝒆𝒓𝒎
𝒅 𝒊𝒔 𝒘𝒉𝒂𝒕 𝒚𝒐𝒖 𝒂𝒓𝒆
𝒂𝒅𝒅𝒊𝒏𝒈 𝒐𝒓 𝒔𝒖𝒃𝒕𝒓𝒂𝒄𝒕𝒊𝒏𝒈
Explicit Formula
𝒇 𝒙 =𝒎𝒙+𝒃
𝒇 𝒙 =𝒅𝒙+𝒇 𝟎
𝒅 𝒊𝒔 𝒔𝒍𝒐𝒑𝒆 𝒇 𝟎 𝒊𝒔 𝒚−𝒊𝒏𝒕
𝒐𝒓 𝒇 𝒙 =𝒅 𝒙−𝟏 +𝒇(𝟏)