The average of 5 consecutive numbers is n. If the next two numbers are also included, the average of the 7 numbers will

Options

A. increase by 2
B. increase by 1
C. remains the same
D. increase by 1.4

Answer

To solve the problem, we need to find the average of 7 consecutive numbers given that the average of the first 5 consecutive numbers is \( n \).

### Step-by-Step Solution:

1. **Define the 5 consecutive numbers**:
Let the first 5 consecutive numbers be \( x, x+1, x+2, x+3, x+4 \).

2. **Calculate the average of the first 5 numbers**:
The average of these 5 numbers can be calculated as:
\[ \text{Average} = \frac{x + (x+1) + (x+2) + (x+3) + (x+4)}{5} \]
Simplifying the numerator:
\[ = \frac{5x + 10}{5} = x + 2 \]
Since we know this average is equal to \( n \):
\[ x + 2 = n \]
Thus, we can express \( x \) in terms of \( n \):
\[ x = n - 2 \]

3. **Define the next two consecutive numbers**:
The next two consecutive numbers after the first 5 are \( x+5 \) and \( x+6 \).

4. **Calculate the average of all 7 numbers**:
Now we need to find the average of the 7 numbers:
\[ \text{Average} = \frac{x + (x+1) + (x+2) + (x+3) + (x+4) + (x+5) + (x+6)}{7} \]
Simplifying the numerator:
\[ = \frac{7x + 21}{7} = x + 3 \]

5. **Substituting \( x \) back in terms of \( n \)**:
We already found that \( x = n - 2 \). Substituting this into the average of the 7 numbers:
\[ x + 3 = (n - 2) + 3 = n + 1 \]

### Final Answer:
Thus, the average of the 7 numbers is:
\[ \boxed{n + 1} \]