We report on our evaluation of field-induced magnetic moments in the paramagnetic state of the spin-12 antiferromagnetic trimerized (J₁-J₂-J₂) chain compound Cu₃(P₂O₆OD)₂ with J₁ = 111 K and J₂ = 30 K [M. Hase et al., Phys. Rev. B 76, 064431 (2007)]. Magnetic reflections with integer indices, generated by field-induced magnetic moments, were observed at neutron-diffraction experiments performed in an applied magnetic field, and we evaluated the magnitudes of the moments to be M₁ = 0.43(2) μ_B/Cu and M₂ = 0.013(10)μ_B/Cu on the two crystallographic Cu²⁺ (Cu1 and Cu2) sites, respectively, at 6 T and 1.6 K. The resulting ratio M₂/M₁ = 0.03(2) is in good agreement with the theoretical value for the ratio of the magnetization at the two sites. We thus conclude that for this well-understood spin system (which has the advantage of being amenable to detailed theoretical calculations) the extracted field-induced magnetic moments reproduce the correct information on the magnetization. Our result leads us to believe that we can precisely evaluate exchange interactions in paramagnets with multiple exchange interactions and multiple crystallographic magnetic-ion sites by using field-induced magnetic moments in combination with macroscopic physical quantities. This idea is expected to be applicable to a wide variety of quantum and frustrated magnets without long-range order.