Pattern Types
What is the difference between a growing and shrinking pattern?
Growing Increases; Shrinking Decreases
Define the words: "Term," "Sequence," "Rule."
Term - One number
Sequence - Ordered numbers
Rule - How the pattern works
What does "n" represent in a table of values?
"n" represents the term number.
What variable is commonly used for term number?
What does slope represent?
Rate of change.
What is a linear pattern?
Write the rule: 6, 11, 16, 21
Start at 6, add 5 each time.
What does a constant rate of change tell us?
That the pattern is linear.
Write the expression for:
6, 11, 16, 21
5n+1
*5(3)+1 = 16*
4
2, 4, 8, 16... Is this a linear or non-linear pattern? How do you know?
Non-linear; the rate of change is exponential.
Write the next 3 terms: 57, 49, 41, 33...
25, 17, 9
What is the rate of change in this table of values?
n t
1 3
2 6
3 9
4 12
+3
1, 2, 3, 4
Negative.
Apples cost $2 per pound. What type of pattern is this?
Linear.
Write the first 5 terms:
Start at 10, double, then subtract 1 each time.
10, 19, 37, 73, 145
Is this pattern linear?
n t
1 4
2 9
3 16
4 25
It is non-linear.
Find the 25th term for:
8, 13, 18, 23
Common Difference = +5
Rule = 5n+3
5(25)+3 = 128
What is the y-intercept in y=7x-2?
-2 (0, -2).
A bunny population doubles each generation. Is this a linear or exponential pattern?
1, 0.5, 0.25, 0.125... Describe the pattern rule.
Start at 1, then divide by 2 each time.
Complete and predict up to the 8th term:
n t
1 7
2 9
3 11
+2 rate of change -> 8th term = 21
Which term would have a value of 100?
4, 10, 16, 22
Common Difference = +6
Rule = 6n-2 (= 100)
6n = 102, n=17
A tradesperson charges a $20 service fee, plus $15 per hour.
Write the equation and what it would cost for 8 hours of work.
Rule: y=15x+20
15(8)+20 = $140