Question

If mean of first n natural numbers is 15, then the value of n is

• A. 15
• B. 30
• C. 14
• D. 29

Answer 1

The Correct Option is D

Step 1: Recall the formula for the mean of the first \( n \) natural numbers.

The sum of the first \( n \) natural numbers is:

\[ S = \frac{n(n + 1)}{2}. \]

The mean of the first \( n \) natural numbers is:

\[ \text{Mean} = \frac{\text{Sum of observations}}{\text{Number of observations}} = \frac{\frac{n(n + 1)}{2}}{n} = \frac{n + 1}{2}. \]

Step 2: Set the mean equal to 15 and solve for \( n \).

\[ \frac{n + 1}{2} = 15. \]

Multiply through by 2:

\[ n + 1 = 30. \]

Solve for \( n \):

\[ n = 30 - 1 = 29. \]

Final Answer: The value of \( n \) is \( \mathbf{29} \), which corresponds to option \( \mathbf{(4)} \).