Quick induced current from magnetic field question direction of current?

With RHR-1, if the rod moves to the right in a field coming into the page, the force will move positive charge up (in reality move negative electrons down) in the rod, and induce a current
but why is the current counter clockwise?

1) Think of the Lorentz force on a charge in a magnetic field, [itex]\vec{F} = q(\vec{v} \times \vec{B})[/itex]. Using the RHR tells you that the force acts upwards along the rod, making the current want to go up the rod and hence counter-clockwise. Taking this a step further, this Lorentz force merely results from an electric field that is set up in a moving conductor in a B-field. This electric field set up across the rod propagates through the rest of the loop, forcing the current to travel in the required direction.

2) Think of Lenz's Law. The current will be set up in the loop in a manner that attempts to counter its cause. The cause in this case, is the increasing flux (B.A) enclosed within the loop as the rod moves to the right. Hence, the current will go in a direction that will try to reduce this flux. So naturally, the current wants to induce a magnetic field in a direction opposite to the existing field. Again, you can use the right hand thumb rule to tell that it takes a counterclockwise current to induce a field coming out of the plane of the paper.