## Understanding of Sequences and their Graphs

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## 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**