Visual Derivation of the Formula for Sum of an Arithmetic Sequence
Subject Area: High School Mathematics, Pre-Calculus Honors
Your Investigation:
1. Use Gauss' method to find the sum of the first one hundred positive integers.
2. Use Gauss' method to derive the formula for the sum of an
arithmetic sequence of n terms whose first term is a
and whose common difference is d.3. Access the web site below, double click on "Sum of an Arithmetical Progression", read the introduction, and work with the "applet".
Questions to Answer:
1. What is the area of each rectangle?
2. How does the area of each rectangle compare to some aspect of the formula for the sum of an arithmetic sequence?
3. What fact is illustrated by the rotation followed by the shift?
4. Explain why the area of the rectangle represents the sum of an arithmetic sequence on n terms, with first term a
and common difference d.Site to Search:
http://www.ies.co.jp/math/java/calcjava.html
Activity created by Farrel Powsner
Roslyn High School
Mathematics Department
farrelp@aol.com