write a sequence for the rule.
1. a - 4 = b
2. a +(2-1) = b
3. a - (3-3)= b
4. a +(4 - 3) = b
5. (a + 2) - 2 = b
6. (a + 4) - (2 -1) = b
To write a sequence for the given rules, let's analyze and simplify each rule.
1. a - 4 = b
In this rule, you subtract 4 from a to get b.
2. a + (2 - 1) = b
Here, you subtract 1 from 2, which equals 1, then add that to a to get b.
3. a - (3 - 3) = b
In this rule, since (3 - 3) equals 0, you don't actually subtract anything from a. Therefore, b would be equal to a.
4. a + (4 - 3) = b
By subtracting 3 from 4, you get 1. This means you add 1 to a to get b.
5. (a + 2) - 2 = b
First, you add 2 to a, and then subtract 2 from the result to obtain b.
6. (a + 4) - (2 - 1) = b
In this last rule, you subtract (2 - 1), which equals 1, from (a + 4). Therefore, b equals (a + 4 - 1).
To write a sequence using these rules, you can start with a given value for a and find the value of b by applying the rules in order.
For example, let's assume a = 3. Using the rules:
1. a - 4 = 3 - 4 = -1
2. a + (2 - 1) = 3 + 1 = 4
3. a - (3 - 3) = 3 - 0 = 3
4. a + (4 - 3) = 3 + 1 = 4
5. (a + 2) - 2 = (3 + 2) - 2 = 3
6. (a + 4) - (2 - 1) = (3 + 4) - 1 = 6
Thus, the sequence for the given rules with a starting value of 3 would be: -1, 4, 3, 4, 3, 6.