The effect of the substitution of one Cu2+ ion (S=1/2) by Mg2+ ion (S=0) on the magnetic property of the linear-chain spin trimer compound Ca3 Cu3 (PO4) 4 was studied using dc magnetic susceptibility in Ca3 Cu2 Mg (PO4) 4 together with those in Ca3 Cu3 (PO4) 4 and Ca3 Cu2 Ni (PO4) 4 for comparison. A remarkable difference is observed among the results obtained in the Mg and the Ni substituted compounds. A clear signature of the reduction in the net spin of the trimers in Ca3 Cu2 Mg (PO4) 4 was found below 65 K, which is compatible with the presence of the Cu2-Cu1-Mg trimers in the singlet ground state, together with those of the type Cu2-Cu1-Cu2 and Mg-Cu1-Mg in the doublet state. However, no signature of the reduction in the net spin of the trimers was observed in Ca3 Cu2 Ni (PO4) 4. This finding suggests that the type of trimers present in Ca3 Cu2 Mg (PO4) 4 and Ca3 Cu2 Ni (PO4) 4 are different. Furthermore, a singlet ground state is partially realized in a quantum spin trimer system Ca3 Cu2 Mg (PO4) 4. {\textcopyright} 2010 The American Physical Society.