examday

/TMUA

A sequence of integers satisfies $u_{n+1}=3u_n-4$, with $u_1$ an integer. Which of the following statements are true?

I: $u_n-2$ is a multiple of $3^{n-1}$ for every $n$.

II: if $u_1$ is even then every term is even.

III: $u_{10}$ is divisible by $3$.