The correct sequence of energy changes taking place in the production of electricity in a hydroelectric dam is:

Potential energy to kinetic energy. The water stored in the reservoir behind the dam has potential energy due to its height. When the water is released, it falls down and gains kinetic energy.

Kinetic energy to mechanical energy. The kinetic energy of the falling water is used to turn the turbines of a generator.

Mechanical energy to electrical energy. The generator converts the mechanical energy of the turbines into electrical energy.

Therefore, the correct sequence is potential energy → kinetic energy → mechanical energy → electrical energy.