Question

an action potential is generated by what?
the sum of hyperpolarizations and depolarizations reaching the axon initial segment and depolarizing the membrane to a level of -65 mv.
when the ion channels allow ions to pass through.
an influx of k+ molecules triggering a sodium - potassium pump to operate completely.
the sum of hyperpolarizations and depolarizations reaching the axon initial segment and polarizing the membrane to a level of 65 mv.

Explanation:

An action potential is generated when the sum of hyperpolarizations and depolarizations reaching the axon initial segment depolarizes the membrane to the threshold potential (around -55 mV in many neurons, not -65 mV as stated in the first option which has a wrong value, but the concept is correct among these options). When ion channels allowing ions to pass through is a more general statement and not the most specific for action - potential generation. An influx of K+ molecules triggering the sodium - potassium pump is not directly related to action - potential generation. Polarizing the membrane to 65 mV is incorrect as action potential occurs when the membrane is depolarized to the threshold and then further depolarizes to a positive value (overshoot), not polarizing to 65 mV.

Answer:

The sum of hyperpolarizations and depolarizations reaching the axon initial segment and depolarizing the membrane to a level of -65 mV (despite the wrong threshold value, the concept is correct compared to others).