Consecutive positive even integers are even numbers that follow each other in order, each separated by a difference of 2.
According to the reference, "Consecutive even integers are even integers that follow each other by a difference of 2." This means that if you start with one even number, the next consecutive even integer is found by adding 2, and so on.
Here's a breakdown:
- Definition: Even integers that follow each other sequentially, increasing by 2 each time.
- Example: 2, 4, 6, 8 are consecutive positive even integers.
- Representation: If x is an even integer, then x + 2, x + 4, x + 6, and x + 8 are consecutive even integers. The reference also mentions that consecutive even integers can be represented by the expression 2n + 2, where n = 0, 1, 2, 3....
Let's illustrate with examples using the expression 2n + 2:
| n | 2n + 2 |
|---|---|
| 0 | 2 |
| 1 | 4 |
| 2 | 6 |
| 3 | 8 |
| 4 | 10 |
As demonstrated, plugging in consecutive non-negative integers for n generates consecutive positive even integers.
