Initially, the parachutist will experience a greater downwards force due to gravity which causes them to accelatae downwards. As they accelarate, the upwards force of air resistance will increase. They will reach a point where the downwards force of their weight is in equillibrium with the upwards force of air resistance. As there is no resultant force, they will no longer accelarate and we can say they have reached their terminal speed.
When they open their parachute,the upwards force of air resistance suddenly increases. The parachutist will start to decelarate. As they slow down, the component of air resistance will decrease relative to their weight until both forces are in equilibrium. The parachutist will now have reached terminal speed.