#### Answer

The numbers are 36, 38, and 40.

#### Work Step by Step

Let n represent the first number; then, n + 2 represents the next even number, and n + 4 the next even number. Because their sum is 114, we can set up and solve the following equation:
n + n + 2 + n + 4 = 114
3n + 6 = 114
Subtract 6 from both sides
3n = 108
Divide both sides by 3
n = 36
If n = 36, then n + 2 = 38, and n + 4 = 40
So, the numbers are 36, 38 and 40.