What Are The Next Three Terms In This Sequence?

Abstract

Continuing a sequence when the first three terms are provided is a problem that students encounter at many levels of instruction. Consider the following: 3, 6, 9, __, __, __.  When asked to fill in the blanks, many students (and more than a few teachers) mistakenly believe that there is only one correct answer. In the following article, the authors explore alternative solutions to such tasks, confirming that—in fact—such questions have many correct answers. Using a mix of by-hand and technology-based approaches, the authors explore three different types of sequences and show how to determine the explicit formula for each based on the term that is chosen next.