Question

The average of 7 consecutive numbers is 20. The largest of these numbers is:

• A. 24
• B. 23
• C. 20
• D. 19

Hint:

For consecutive numbers, the average is the middle number. If you know the average, you can find the largest number by adding \( \text{(half the total number of terms minus 1)} \) to the first number.

Answer 1

The Correct Option is B

Step 1: Representing the 7 consecutive numbers.
Let the 7 consecutive numbers be \( x, x+1, x+2, x+3, x+4, x+5, x+6 \), where \( x \) is the first number. Step 2: Understanding the formula for the average of these numbers.
The average of these 7 consecutive numbers is: \[ \text{Average} = \frac{x + (x+1) + (x+2) + (x+3) + (x+4) + (x+5) + (x+6)}{7}. \] Simplifying the sum of these numbers: \[ \text{Average} = \frac{7x + 21}{7} = x + 3. \] Step 3: Using the given average to find \( x \).
We are told that the average is 20, so: \[ x + 3 = 20. \] Solving for \( x \): \[ x = 20 - 3 = 17. \] Step 4: Finding the largest number.
The largest of these 7 numbers is: \[ \text{Largest number} = x + 6 = 17 + 6 = 23. \] Thus, the largest number is \( 23 \).