Presupunem prin absurd ca √5,√7,√10 sunt termeni consecutivi ai unei progresii aritmetice =>
√7=√5+√10 /2 => 2√7=√5+√10 <=>28=(√5+√10)² <=> 28=15+2√50 <=>
28=15+10√2 <=> 10√2=13 <=> 200=169, contradictie, asadar √5,√7,√10 nu formeaza o progresie aritmetica.