Number Sequences in Desmos
Desmos is a fantastic tool for teachers and maths enthusiasts alike. This is a collection of sequences that I have set up in the Desmos…
Number Sequences in Desmos
Desmos is a fantastic tool for teachers and maths enthusiasts alike. This is a collection of sequences that I have set up in the Desmos Graphing Calculator. I hope that you will find these useful in your teaching or numerical investigations.
Table of Contents
- Linear sequences
- Triangular sequences
- Square sequences
- Cube sequences
- Geometric sequences
- Quadratic sequences
Linear sequences
Linear sequences a.k.a. Arithmetic sequences can be generated with the following n-th term rule:
where, a is the first term, d is the common difference, and n is the position index.
However, linear sequences are taught this way in secondary schools:
where, a is the constant term, and d is the common difference that we add on term-to-term. In this case, a+d forms the first term.
Here is the desmos model for the school approach:
Triangular sequences
Visually, if you stack dots for each term in a triangular sequence {1, 3, 6, 10, 15, …}, each dot stack will form an unmistakeable triangular pattern, increasing by n dots each iteration.
Triangle numbers follow this formula:
where, n is the location in the sequence.
Square sequences
Stack dots for each number in the square sequence {1, 4, 9, 16, 25, …} in a n-by-n grid to form square patterns.
Square numbers follow the n-th term formula:
where, n is the position in the sequence.
Cube sequences
If we stack the numbers {1, 8, 27, 64, 125, …} as collections of unit cubes in a n-by-n-by-n formation, these stack should construct the familiar cubes.
The cubed numbers follow this formula:
where, n is the positional index.
Geometric sequences
One of the most common sequences in finance, economics and scientific modelling, is the geometric sequence. These have a common ratio r. Each term is the previous term multiplied by this common ratio. For example, if we halve each subsequent term then the ratio is 1/2.
T(n)=(1/2)^(n-1)
The general geometric term looks as this:
where, a is the first term, r is the common ratio, and n is the positional index. Here is the demo in desmos:
Quadratic sequences
Starting in Year 9 throught to GCSE exams and AS-Levels, students learn about quadratic sequences which are formed using the standard equation for a parabola i.e., y = ax² + bx + c.
These sequences along with the famous quadratic equation are met frequently in science and engineering, therefore very useful for students to get to grips with ‘quadratics’.
T(n) = n²-2n+4
Here is the demo in desmos for quadratic sequences:
As a bonus, I have included my quadratic analysis tool that I have set up in desmos as well. Have fun!
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