State if the result is always odd or always even:
Two consecutive odd numbers are added

Answer

To determine whether the sum of two consecutive odd numbers is always odd or always even, we can follow these steps:

### Step 1: Define the consecutive odd numbers
Let the first odd number be represented as \( n \). Since we are dealing with consecutive odd numbers, the next consecutive odd number can be represented as \( n + 2 \).

### Step 2: Write the expression for their sum
Now, we can write the sum of these two consecutive odd numbers:
\[ \text{Sum} = n + (n + 2) \]

### Step 3: Simplify the expression
Now, let's simplify the expression:
\[ \text{Sum} = n + n + 2 = 2n + 2 \]

### Step 4: Factor the expression
We can factor out the common term:
\[ \text{Sum} = 2(n + 1) \]

### Step 5: Analyze the result
The expression \( 2(n + 1) \) indicates that the sum is a multiple of 2. Since any multiple of 2 is even, we can conclude that the sum of two consecutive odd numbers is always even.

### Conclusion
Thus, the result of adding two consecutive odd numbers is always even.

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