Aim # 42: What is an arithmetic sequence?
Do Now: Answer the following based on the figures below.
figure 1
figure 2
figure 3
figure 4
A) How many boxes are there in figure 1?
B) How many boxes are there in figure 2?
C) How many boxes are there in figure 3?
C) What is the pattern?
D) If we created a figure 5, how many boxes should there be?
E) If we created a figure 0, how many boxes should there be?
Let's let x represent the figure number, and f(x) represent the number of
boxes in figure x.
Create a table of values
x
f(x)
0
1
2
3
4
5
6
What is the slope?
What is the y-intercept?
Graph the points from the table
figure 0
figure 2
figure 1
figure 3
figure 4
What is the pattern?
Create a table
Graph the points
What is the slope?
What is the y-intercept?
A sequence is an ordered set of mathematical objects.
An ___________ sequence is a sequence where the same number is added each
time to get the next term.
The same number that is added each time is called ___, the common difference.
An arithmetic sequence can be modeled by y = mx + b.
m=
b=
A few terms of a sequence are shown below.
Is this sequence arithmetic? How do we know?
What is the common difference?
If we created a figure 0, how many boxes would it have?
Create a function to represent the number of boxes in figure x.
Use your function to calculate the number of boxes in figure 4.
The growth of a tile Pattern W is represented by the equation y = 3x + 1.
A. Copy and fill in the table for Pattern W.
B. By how many tiles is Pattern C growing?
C. What is the starting value?
D. Where do you look in the table to see the growth and starting value?
E. Where do you look in the equation to see the growth and starting value?
Compare the sequence below to Pattern W from above.
Figure # # of tiles
0
4
1 7
2 10
3 13
How are they the same?
How are they different?
What is the equation that models this sequence?
How does this equation compare to the equation for Pattern W?
Let's sum it up!!!
A sequence is an ____________ set of objects.
An arithmetic sequence has a pattern where we _____ the same amount each
time
To create an equation for an arithmetic sequence we use y = mx + b. The m value
is the same as ___ and the b value is the same as the value for figure ___.