n Learning and Teaching Mathematics - The heuristic beauty of figural patterns

Volume 2012, Issue 12
  • ISSN : 1990-6811


I am generally left with a sense of unease whenever I encounter questions of the type shown below:

Write down the next three terms in the following sequence: 2 ; 6 ; 12 ; ...
My disquiet with such questions stems from the basic observation that any finite sequence of numbers can be justifiably continued in an infinite number of ways. Thus, any arbitrary choice of "the next three terms" should be given full credit. However, there seems to be a general acceptance that such questions are underscored by an unstated proviso that the three terms required should represent the "most obvious" or "most logical" sequence - whatever that's supposed to mean! Those questions that are prefaced, presumably with good intentions, with something along the lines of "Given that the following pattern continues in the same way..." are even more irksome, since there's an assumption that the "obvious" pattern is indeed that, i.e. "obvious", whereas I would argue that this notion is nonsensical. This can be understood by taking cognizance of the fact that a finite numeric sequence can be generated by an infinite number of functions, an idea that is readily supported by considering a finite number of points plotted in the Cartesian Plane where there would clearly be an infinite number of curves that could be drawn through the specified points. Thus, no finite sequence of numerical terms uniquely specifies the following term in a given sequence.

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