Select the correct graphical representation :

The graph is plotted between the ionic radius and atomic number.
Lanthanide series includes the 14 elements from the atomic numbers 58 through 71,The lanthanide elemnt are cerium, praseodymium, neodymium, promethium, samarium, europium, gadolinium, terbium, dysprosium, holmium, erbium, thulium, ytterbium, and lutetium.
 

As we know that on going from left to right the atomic radius is increasing. While the ionic radius decreases.

Because the effective nuclear charge increases.
 

As the ionic radius is inversly propotional to the atomic radius. A negative slope on a linear graph or a downward descending curve on a graph indicates an inverse connection.

Hence the graph A is correct.