Question

If the mean of four consecutive odd numbers is 6 then the largest number is

• A. 5
• B. 9
• C. 21
• D. 15

Hint:

For an even number of consecutive terms in an arithmetic progression, the mean is the average of the two middle terms. The four numbers are 3, 5, 7, 9. The middle two are 5 and 7. Their mean is \((5+7)/2 = 6\), which matches the given information. The largest is 9.

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
Consecutive odd numbers differ by 2. We can represent them algebraically, set up an equation for their mean, solve for the variable, and then find the largest number.

Step 2: Key Formula or Approach:
Let the four consecutive odd numbers be \(x\), \(x+2\), \(x+4\), and \(x+6\).
The mean (average) is the sum of the numbers divided by the count of the numbers.
\[ \text{Mean} = \frac{x + (x+2) + (x+4) + (x+6)}{4} \]

Step 3: Detailed Explanation:
We are given that the mean is 6.
\[ 6 = \frac{x + x+2 + x+4 + x+6}{4} \] \[ 6 = \frac{4x + 12}{4} \] Multiply both sides by 4:
\[ 24 = 4x + 12 \] Subtract 12 from both sides:
\[ 12 = 4x \] Solve for \(x\):
\[ x = 3 \] The numbers are:
First number: \(x = 3\)
Second number: \(x+2 = 5\)
Third number: \(x+4 = 7\)
Fourth (largest) number: \(x+6 = 9\)

Step 4: Final Answer:
The largest number is 9.