Question

Let $P\left(n\right)=n(n+1)(n+2)$ is divisible by $12$ then which one of the following is not true.

i) $P\left(3\right)$

ii) $P\left(4\right)$

ii) $P\left(5\right)$

iv) $P\left(8\right)$

Answer 1

Given, $P\left(n\right)=n(n+1)(n+2)$.

Now,

i) $P\left(3\right)=\mathrm{3.4.5}=60$ is divisible by $12$.

ii) $P\left(4\right)=\mathrm{4.5.6}=120$ is divisible by $12$.

iii) $P\left(5\right)=\mathrm{5.6.7}=210$ not divisible by $12$.

iv) $P\left(8\right)=\mathrm{8.9.10}=720$ is divisible by $12$.

So $P\left(5\right)$ is not true.