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

The mean (average) of the first n natural numbers 1, 2, 3, …, n is the sum of these numbers divided by their count. Since the sum of the first n natural numbers equals n(n + 1)/2, dividing by n gives the mean as (n + 1)/2.

1. Write the mean formula for the first n natural numbers: Mean = (n + 1)/2.

2. Substitute the given mean value 15 into the formula: (n + 1)/2 = 15.

3. Multiply both sides by 2: n + 1 = 30.

4. Subtract 1 from both sides to isolate n: n = 29.

Substituting n = 29 back into the formula gives (29 + 1)/2 = 30/2 = 15, which matches the mean stated in the question, confirming that n = 29 is correct.