Predicting Terms in Repeating Patterns
Identify the pattern core in the following repeating pattern:
B M X W B M X W B M...
B M X W
What would the 9th term in the following pattern be:
8, 12, 16, 20...
40
Using x and y variables, create an equation for the following pattern:
3, 5, 7, 9, 11...
MAKE SURE TO WRITE OUT THE COMPLETE EQUATION
y = 2x + 1
In an ordered pair, is the y coordinate first or second?
Second!
Put the following ordered pairs into a table of values (in the proper order for a growing pattern). Remember to label each column
(3, 7)
(4, 9)
(2, 5)
(1, 3)
x |. y
_____
1. |. 3
_____
2. |. 5
_____
3. |. 7
_____
4. |. 9
The following pattern repeats:
D E F D E F D E...
What will the 33rd Term be? How do you know?
F
...Because the pattern core has 3 terms, meaning every term number that is a multiple of 3 will be the final term in the core. 33 is a multiple of 3 and the final term in the core is F.
What would the zero term be of the following pattern?
8, 15, 22, 29, 36
1
Using x and y variables, create an equation for the following pattern:
4, 9, 14, 19, 24...
MAKE SURE TO WRITE OUT THE COMPLETE EQUATION
y = 5x - 1
Which quadrant of the Cartesian Plane would the ordered pair (-44, 4) be in?
Quadrant 2
The following ordered pairs are for a growing pattern, describe the pattern they show (in words):
(4, 25); (2, 11); (5, 32); (1, 4); (3, 18)
Start at 4, increase by 7 each time
The following pattern continues:
Q R S T Q R S T Q...
What is the 43rd term in the pattern? How do you know?
S
...because there are 4 terms in the pattern core, so each term number that is a multiple of 4 will be the last term in the core (which is T). 43 is not a multiple of 4, but 44 is. The 44th term would be T, making the 43rd term S
What would the 20th term in the following pattern be?
20, 26, 32, 38, 44...
134
Using x and y variables, create an equation for the following pattern:
6, 15, 24, 33, 42...
MAKE SURE TO WRITE OUT THE COMPLETE EQUATION
y = 9x - 3
Which quadrant of the Cartesian Plane would the ordered pair (67, -77) be in?
Quadrant 4
The following ordered pairs are for a growing pattern, describe the pattern they show (in words):
(5, 23); (1, 7); (3, 15); (6, 27); (2, 11)
Start at 7, increase by 4 each time
The following pattern continues:
K L O K L O K L O K ...
What would the 52nd term be? How do you know?
...Because term 51 would be O, as 51 is a multiple of 3. There are 3 terms in the pattern core, making every term that is a multiple of 3 O. K always follows O in the pattern, therefore the 52nd term would be K
What would the zero-term be for the following pattern?
6, 14, 22, 30, 38...
-2
Using x and y variables, create an equation for the following pattern:
7, 24, 41, 58...
MAKE SURE TO WRITE OUT THE COMPLETE EQUATION
y = 17x - 10
The ordered pair (0, -9) would be plotted on the _____________
The Y-Axis
The following ordered pairs are for a growing pattern, using x and y variables determine an equation to represent the pattern:
(3, 16); (5, 26); (1, 6); (4, 16)
y = 5x + 1
The following pattern continues:
F L O W F L O W F...
What would the 66th term in the pattern be? How do you know?
L
...because every term that is a multiple of 4 would be the last term in the pattern core - W. 64 is a multiple of 4, making the 64th term W. L is always the term two after W, therefore the 66th term would be L.
What would the 84th term of the following pattern be?
3, 7, 11, 15, 19, 23, 27...
335
Using x and y variables, create an equation for the following pattern:
-5, 8, 21, 34, 47, 60...
MAKE SURE TO WRITE OUT THE COMPLETE EQUATION
y = 13x - 18
- the 4 quadrants
- y AND x axis
- whether the x and y coordinates would be positive or negative
- arrowheads
^ y-axis
Quadrant 2 |. Quadrant 1
(-x, +y) |. (+x, +y)
<____________________________> x-axis
Quadrant 3 |. Quadrant 4
(-x, -y) |. (+x, -y)
v
The following ordered pairs are for a growing pattern, using x and y variables determine an equation to represent the pattern:
(4, 40); (6, 62); (1, 7)
y = 11x - 4