Yes, this neuron will produce an action potential at this time.
An action potential may be defined as the transformation in electrical potential associated with the passage of an impulse along the membrane of a nerve cell or muscle cell.
All the potential changes at the three synapses have halved i.e. +20 mV originated at synapse 1, +10 mV originated at synapse 2, and -5mV originated at synapse 3. The sum of all potential is +25mV.
The neuron required a minimum change of +20mV.
∴ -70mV + (+20mV) = -50mV.
Hence, it will terminate an action potential.
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