Finding the General Term for an Arithmetic Progression: Alternatives to the Formula

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Australian Mathematics Teacher, v66 n2 p17-21 2010

Secondary school students in Singapore are expected to find an expression for the general or "nth" term of an arithmetic progression (AP) without using the AP formula T[subscript n] = a + (n-1)d, where "a" is the first term, "n" is the number of terms and "d" is the common difference between successive terms. This type of question is worth only one mark in the GCE O-Level Examination but the usual method taught in school is far too long and many students feel that it is not worth trying so hard for one mark. This led the author, when he was a teacher, to look for other shorter methods. In this article, he will discuss five methods to find an expression for the "nth" term of an AP, including arguably the fastest method that he has invented. He believes teachers will not only find the "fastest" method useful for their students but they can also challenge their students to be innovative and creative: find as many methods as possible to find the general term of an AP.

Descriptors: Foreign Countries, Secondary School Students, Arithmetic, Pattern Recognition, Teaching Methods

Australian Association of Mathematics Teachers (AAMT). GPO Box 1729, Adelaide 5001, South Australia. Tel: +61-8-8363-0288; Fax: +61-8-8362-9288; e-mail: office[at]aamt.edu.au; Web site: http://www.aamt.edu.au

Autor: Yeo, Joseph B. W.

Fuente: https://eric.ed.gov/?q=a&ft=on&ff1=dtySince_1992&pg=3692&id=EJ891794