Understanding of Sequences and their Graphs


Kyungsoon Jeon


Students have studied various kinds of functions like the linear, quadratic, cubic, exponential, logarithmic, trigonometric functions during their middle and high school years. They have learned the function of variables and also encouraged to find the best fitting curve when a certain set of data is given. This essay is to provide a deeper understanding of sequences in terms of their graphical interpretation under the condition that students have a knowledge of the various functions. Students will explore the three types of sequence and their graphs with a spreadsheet. What are the shapes of an arithmetic, harmonic, geometric sequence? How are they related with the specific functions? The three spread sheet files which is in the essay-3 folder will be able to explain many things to the students. The sequences in "arithmetic sequence" are all arithmetic sequences. In particular, students can compare the difference of three graphs with different increases of the sequences. The graphs are all linear functions. The second file entitled "harmonic sequence" shows two types of functions. One is expressed by f(n)=6/n and a harmonic sequence. The other is described by f(n)=n/6 and an arithmetic sequence. It is interesting to compare two type of sequences at the same time. The third file is about geometric sequences. Two sequences shows the different directions. Students are encouraged to understand the shapes of two sequences in the view point of the exponential function.



activity 1: arithmetic-sequence


activity 2: harmonic-sequence


activity 3: geometric-sequence