The variance of $\hat{\theta}_n$ is constant regardless of $n$.

The variance of $\hat{\theta}_n$ behaves like $V(\theta)/n$ for large $n$.

The variance of $\hat{\theta}_n$ converges to $V(\theta)$ as $n \to \infty$.

The variance of $\hat{\theta}_n$ decreases at a rate of $1/\sqrt{n}$.