Question

Let $P\left(n\right)$ be the statement representing the sum of next three successive natural numbers of $n$, $\forall n\in N$, then the smallest value of $n$ to which $P\left(n\right)$ is divisible by $9$ is

• A. $1$
• B. $3!$
• C. $3$
• D. $9!$

Answer 1

The correct option is A $1$

As $p\left(n\right)=(n+1)+(n+2)+(n+3)$
$p\left(n\right)=3n+3+3=3(n+2)$
$\therefore p\left(1\right)=3\left(3\right)=9$ which is divisible by 9
$\therefore$ least value of $n$ is $1$.
Ans: A