Final answer:
The most appropriate medication to administer at the next rhythm check would be amiodarone.
Step-by-step explanation:
If the rhythm of the patient persists at the next rhythm check, the most appropriate medication to administer at that time would be amiodarone.
Amiodarone is an antiarrhythmic medication commonly used in pulseless arrest situations. It works by stabilizing the electrical activity of the heart and restoring a normal rhythm.
Other medications that may be considered in this situation include lidocaine and magnesium sulfate, depending on the specific characteristics of the patient's arrhythmia.