Are sober noetherian spaces sequential?

Question

A sequential topological space $X$ has a few different equivalent definitions:

1. $X$ is the quotient of a first-countable space
2. $X$ is the quotient of a metric space
3. Sequentially open subsets of $X$ are open
4. Sequentially closed subsets of $X$ are closed
5. For every subset of $X$ that is not closed, there is a convergent sequence to a point outside the subset
6. Any sequentially continuous function from $X$ to another space is continuous
7. The topology is the final topology with regards to all continuous maps from the one-point compactification of $\mathbb{N}$, i.e. convergent sequences in $X$, so those generate the topology

The Wikipedia article on sequential spaces claims that the spectrum of any noetherian ring is sequential. It does not provide a reference for this, is there one? Alternatively, is there a short proof of this statement? The most straightforward translation to a purely topological statement would be whether sober noetherian spaces are sequential.