Question

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

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

Answer 1

The Correct Option is B

To solve the problem of determining how the average changes when including two additional numbers in the sequence, we need to start by understanding what is being asked: Given that the average of 5 consecutive numbers is \( n \), how does including the two subsequent consecutive numbers affect the average?

Let the 5 consecutive numbers be \( x, x+1, x+2, x+3, \) and \( x+4 \). The average of these numbers is given by:

\[ \text{Average} = \frac{x + (x+1) + (x+2) + (x+3) + (x+4)}{5} = \frac{5x + 10}{5} = x+2 \]

It's mentioned that this average is \( n \), so we have:

\[ x+2 = n \implies x = n-2 \]

Now, including the next two consecutive numbers, which are \( x+5 \) and \( x+6 \), makes the numbers:

\( x, x+1, x+2, x+3, x+4, x+5, x+6 \).

The new average is calculated as follows:

\[ \text{New average} = \frac{x + (x+1) + (x+2) + (x+3) + (x+4) + (x+5) + (x+6)}{7} = \frac{7x + 21}{7} = x+3 \]

Since \( x = n-2 \), we substitute back to find:

\[ \text{New average} = (n-2) + 3 = n+1 \]

Therefore, the average increases by 1 when the next two numbers are included.

Thus, the correct choice is: increase by 1.