(The average of five consecutive (numbers)integer starting from m) - (the average of six consecutive integers starting from m) =

Answer

To solve the problem step by step, we will find the average of five consecutive integers starting from \( m \) and the average of six consecutive integers starting from \( m \), and then subtract the two averages.

### Step 1: Identify the five consecutive integers starting from \( m \)
The five consecutive integers starting from \( m \) are:
- \( m \)
- \( m + 1 \)
- \( m + 2 \)
- \( m + 3 \)
- \( m + 4 \)

### Step 2: Calculate the average of the five consecutive integers
To find the average, we sum these integers and divide by 5:
\[ \text{Average of 5 integers} = \frac{m + (m + 1) + (m + 2) + (m + 3) + (m + 4)}{5} \]
Calculating the sum:
\[ = \frac{5m + (0 + 1 + 2 + 3 + 4)}{5} = \frac{5m + 10}{5} = m + 2 \]

### Step 3: Identify the six consecutive integers starting from \( m \)
The six consecutive integers starting from \( m \) are:
- \( m \)
- \( m + 1 \)
- \( m + 2 \)
- \( m + 3 \)
- \( m + 4 \)
- \( m + 5 \)

### Step 4: Calculate the average of the six consecutive integers
To find the average, we sum these integers and divide by 6:
\[ \text{Average of 6 integers} = \frac{m + (m + 1) + (m + 2) + (m + 3) + (m + 4) + (m + 5)}{6} \]
Calculating the sum:
\[ = \frac{6m + (0 + 1 + 2 + 3 + 4 + 5)}{6} = \frac{6m + 15}{6} = m + 2.5 \]

### Step 5: Subtract the average of the six integers from the average of the five integers
Now we need to find:
\[ \text{Result} = (m + 2) - (m + 2.5) \]
Simplifying this:
\[ = m + 2 - m - 2.5 = 2 - 2.5 = -0.5 \]

### Final Answer
Thus, the result is:
\[ \text{Result} = -\frac{1}{2} \]

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