How does an arrow move if it is motionless at every instant?

In the limit, not the instant. The dichotomy paradox, which says a distance cannot be covered because it requires infinitely many half-steps first, waited on calculus and the proof that infinite geometric series can converge. The infinite number of half-steps is balanced by the increasingly short time each one takes.

Zeno’s paradoxes are a set of four, dealing with counterintuitive aspects of continuous space and time. They are arguments rather than observations, each built to make ordinary motion look impossible.

The dichotomy comes first. Before an object can travel a given distance it must travel half of it, and before that half of the half, and since the sequence goes on forever the distance appears untraversable.

That one has a clean answer. The resolution awaited calculus and the proof that infinite geometric series can converge, so that the infinite number of half-steps needed is balanced by the increasingly short amount of time required to traverse each distance.

The arrow is different in kind. A flying arrow has an instantaneous position at a given instant of time, at which it is indistinguishable from a motionless arrow in the same place. That asks what motion means inside an instant, rather than how a series sums.