Psychologisches Institut der Universität Heidelberg
This article deals with the problems of existence and uniqueness of solution in connection with number sequence tasks (often called ''number-series completion tasks'') that are widely used in various psychological contexts. It is argued that the problems of existence and uniqueness of solution can be rationally analyzed and controlled only when each type of sequence task applied is explicitly referred to some domain of permissible rules accounting for the included sequence type. Following this guideline, the class of linear-recursive number sequence tasks is introduced where the sequence members are related by linear recursive equations. The investigation of this type of sequence task can substantially profit from the theory of linear equation systems. The analysis carried out uncovers several types of non-uniqueness of solution. Most striking is the fact that worst cases of non-uniqueness may occur even in strongly restricted subtypes of linear-recursive number sequences as is shown for a specific type of task. The results of the analyses suggest that (number) sequence tasks should not be applied in psychological contexts if not accompanied by an instruction that refers explicitily to some domain of permitted sequence rules.
Key words: number series -- number-series completion tasks -- linear-recursive number sequences -- existence and uniqueness of solution