If a, b and c are consecutive integers, what is `a+b+c`?

Answer

To solve the problem of finding the sum of three consecutive integers \(a\), \(b\), and \(c\), we can follow these steps:

### Step-by-Step Solution:

1. **Define the Consecutive Integers:**
Let \(x\) be an integer. We can represent three consecutive integers as:
- \(a = x - 1\)
- \(b = x\)
- \(c = x + 1\)

2. **Write the Expression for the Sum:**
Now, we need to find the sum \(a + b + c\):
\[ a + b + c = (x - 1) + x + (x + 1) \]

3. **Simplify the Expression:**
Combine the terms:
\[ a + b + c = x - 1 + x + x + 1 = 3x \]

4. **Determine the Nature of the Sum:**
The sum \(3x\) can be either odd or even depending on the value of \(x\):
- If \(x\) is odd, then \(3x\) is odd (since the product of two odd numbers is odd).
- If \(x\) is even, then \(3x\) is even (since the product of an odd number and an even number is even).

5. **Conclusion:**
Therefore, the sum \(a + b + c\) can either be odd or even, depending on whether \(x\) is odd or even.

### Final Answer:
The sum \(a + b + c = 3x\) can be either odd or even.