Young and older adults were asked to verify true (e.g., 5 x 61 = 305) and false (5 x 61 = 315) arithmetic problems. Half the problems were small (e.g., 5 x 17 = 85) and half were large problems (e.g., 5 x 93 = 465). Half the false problems respected the five rule (i.e., the product of an operand multiplied by five ends with either 5 or 0), and half violated this rule (e.g., 21 x 5 = 115 vs. 21 x 5 = 113). Both young and older adults showed problem-size effects (i.e., they verified small problems more quickly than large problems) and five-rule violation effects (i.e., they verified problem violating five rule more quickly than problems respecting five rule). Moreover, we found sequential modulations of these problem-size and five-rule effects. Problem-size effects were larger on current problems following large problems than after small problems, and five-rule violation effects were larger after problems violating the five rule than after no-rule violation problems. Finally, sequential modulations of problem-size effects were larger in older adults than in young adults, and there were no age-related differences in sequential modulations of five-rule violation effects. These findings speak to the determiners of arithmetic performance, as to how well arithmetic calculation and non-calculation strategies are executed and selected on current problems depends on strategies used with preceding problems.