1. Finding the Rule
Algebraic patterns

2. Finding the rule – guess & checkx y 1 7 2 14 3 21 4 28 5 35
X 7

3. Finding the recursive rule
A recursive rule is one which can be applied over and over again to its own output
Eg , 127, 130, 133, 136 (recursive rule is + 3)
Eg. 29, 19, 9, -1, -11, -21 (recursive rule is -10) x y 15 30 16 31 17 32 18 33 19 34
Recursive rule is + 1

4. Finding the input/output rulex y 15 30 16 31 17 32 18 33 19 34
y = x + 15

5. Finding the input/output rule (continued)x y 1 9 2 11 3 13 4 15 5 17
What is the recursive rule?
+ 2
This recursive rule gives us a clue to the input/output rule.
y = mx + c
m = recursive rule
y = 2x + c
Therefore y = 2x + 7

6. Finding the input/output rule Try your ownx y 1 6 2 11 3 16 4 21 5 26
First, find the recursive rule.
The recursive rule tells us the multiplier (m).
y = mx + c

7. Try another one x y 1 10 2 18 3 26 4 34 5 42

8. Go the other way x y 1 ? 2 3 4 5 10 40
100
y = 10x + 5