The electronic configurations of the given lanthanoids are based on the general configuration $[\text{Xe}] 4f^{1-14} 5d^{0-1} 6s^2$:

• Europium (Eu, Z = 63): The nearest noble gas is Xenon ($Z=54$). It has 9 valence electrons. Due to the extra stability of a half-filled f-subshell, its configuration is $[\text{Xe}] 4f^7 6s^2$.
• Gadolinium (Gd, Z = 64): It has 10 valence electrons. To maintain the highly stable half-filled $4f^7$ configuration, the additional electron enters the $5d$ orbital. Thus, its configuration is $[\text{Xe}] 4f^7 5d^1 6s^2$.
• Terbium (Tb, Z = 65): It has 11 valence electrons. The $5d$ electron shifts back to the $4f$ subshell as the $4f$ energy level becomes lower, resulting in the configuration $[\text{Xe}] 4f^9 6s^2$.