If the sum of three consecutive numbers is 15, what is the square of the middle number?

Options

A. 16
B. 25
C. 36
D. Cannot be determined

Explanation

To solve the problem of finding the square of the middle number when the sum of three consecutive numbers is 15, we can follow these steps:

### Step-by-Step Solution:

1. **Define the Consecutive Numbers**:
Let the first consecutive number be \( x \). Therefore, the three consecutive numbers can be expressed as:
- First number: \( x \)
- Second number: \( x + 1 \)
- Third number: \( x + 2 \)

2. **Set Up the Equation**:
According to the problem, the sum of these three consecutive numbers is equal to 15. We can write this as:
\[ x + (x + 1) + (x + 2) = 15 \]

3. **Simplify the Equation**:
Combine like terms:
\[ x + x + 1 + x + 2 = 15 \]
This simplifies to:
\[ 3x + 3 = 15 \]

4. **Isolate \( x \)**:
To solve for \( x \), subtract 3 from both sides:
\[ 3x = 15 - 3 \]
\[ 3x = 12 \]
Now, divide both sides by 3:
\[ x = \frac{12}{3} = 4 \]

5. **Find the Middle Number**:
The middle number is \( x + 1 \):
\[ x + 1 = 4 + 1 = 5 \]

6. **Calculate the Square of the Middle Number**:
Now, we need to find the square of the middle number:
\[ (x + 1)^2 = 5^2 = 25 \]

### Final Answer:
The square of the middle number is \( 25 \).