Question

If the arithmetic mean of first $n$ natural numbers is $15$, then $n$ is equal to:

• A. $15$
• B. $20$
• C. $14$
• D. $29$

Answer 1

Answer: (D)

$29$

The first $n$ natural numbers are $1,2,3,...,n$

Given that mean of $n$ natural numbers is $15$

$⟹\frac{1+2+3+...+n}{n}=15$ ———(1)

We know that sum of first $n$ natural numbers is $\frac{n(n+1)}{2}$

$⟹1+2+3+...+n=\frac{n(n+1)}{2}$ ———(2)

Substituting (2) in (1) we get

$⟹\frac{n(n+1)}{2n}=15$

$⟹n+1=30⟹n=30-1=29$