w, x, y, z are four consecutive odd numbers. Their average is

Options

A. (a) w + 2
B. (b) w + 3
C. (c) w + 4
D. (d) w + 6

Answer

To find the average of four consecutive odd numbers \( w, x, y, z \), we can follow these steps:

### Step 1: Define the first odd number
Let the first odd number be \( w \).

### Step 2: Express the consecutive odd numbers
Since they are consecutive odd numbers, we can express the next three odd numbers as:
- \( x = w + 2 \) (the second odd number)
- \( y = w + 4 \) (the third odd number)
- \( z = w + 6 \) (the fourth odd number)

### Step 3: Write the sum of the four numbers
Now, we can find the sum of these four numbers:
\[ \text{Sum} = w + x + y + z = w + (w + 2) + (w + 4) + (w + 6) \]
This simplifies to:
\[ \text{Sum} = w + w + 2 + w + 4 + w + 6 = 4w + 12 \]

### Step 4: Calculate the average
To find the average, we divide the sum by the number of terms (which is 4):
\[ \text{Average} = \frac{\text{Sum}}{4} = \frac{4w + 12}{4} \]
This simplifies to:
\[ \text{Average} = w + 3 \]

### Final Answer
Thus, the average of the four consecutive odd numbers \( w, x, y, z \) is \( w + 3 \).

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