Question

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

• A. 24
• B. 20
• C. 23
• D. 22

Hint:

For 7 consecutive numbers with average 20: Middle is 20, smallest is $20-3=17$, and largest is $20+3=23$.

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
For an odd number of consecutive integers in arithmetic progression, the average equals the exact middle number.

Step 2: Key Formula or Approach:
Let the 7 consecutive numbers be $x-3, x-2, x-1, x, x+1, x+2, x+3$.
The middle number (4th term) is the average, so $x = 20$.
The complete set of 7 consecutive integers is $17, 18, 19, 20, 21, 22, 23$.

Step 3: Detailed Explanation:
The largest number in the series is:
\[\text{Largest} = x + 3 = 20 + 3 = 23\]

Step 4: Final Answer:
Thus, the largest number is 23.