Question

The average of five consecutive numbers is $n$. If the next two numbers are also included, then the average will–

• A. remain the same
• B. increase by one
• C. increase by 1.4
• D. increase by 2

Hint:

For consecutive numbers, the average is the middle number. Adding more consecutive numbers on one side shifts the average towards that side. If the same number of terms is added to both sides, the average remains unchanged.

Answer 1

The Correct Option is C

Step 1: Represent the 5 consecutive numbers.
Let the 5 consecutive numbers be: \[ n-2, n-1, n, n+1, n+2 \] Their sum is: \[ (n-2) + (n-1) + n + (n+1) + (n+2) = 5n \] The average is: \[ \frac{5n}{5} = n \] This matches the given information. 
Step 2: Include the next two consecutive numbers.
The next two numbers after $n+2$ are: \[ n+3, n+4 \] Now the 7 numbers are: \[ n-2,\ n-1,\ n,\ n+1,\ n+2,\ n+3,\ n+4 \] 
Step 3: Find the new sum and average.
New sum: \[ 5n + (n+3) + (n+4) = 5n + 2n + 7 = 7n + 7 \] New average: \[ \frac{7n + 7}{7} = n + 1 \] Wait — This suggests an increase of $1$, so let's double-check the interpretation. 
Step 4: Careful check — Why not 1?
Actually, the average of the first 5 numbers is $n$ (middle term), so $n$ is exactly the third number. Adding two higher numbers pulls the average up. 
But here, $n$ is given as the average, not necessarily the middle term value of the original set (though for consecutive numbers it is). This means the direct calculation is valid — the increase is: \[ (n+1) - n = 1 \] So the correct increase is $1$, not $1.4$. \[ \boxed{\text{Increase by 1}} \]