Maths SL, Type 1 Portfolio - triangular numbers

by meddakik (student)

Maths Practice Portfolio

Maths Portfolio Type I

Special numbers go back in history and there is a great relation between the theorists and the maths they discovered. They are numbers with unique properties, making them different to other ordinary numbers. ‘The origins of the concept of the shape of number’ is a topic which can be directly related to this fact. The idea behind this is that there are many origins of the concept of the shape of number. In the following task we were investigating patterns in geometric shapes that will lead to the formation of special numbers. More specifically, we will look at triangular patterns that will enable us to discover a pattern of special numbers. The first part of the investigation we looked at a triangular pattern formed with dots in the shape of triangles to and calculates the nth term for this pattern.

Original Sequence

Counting the number of dots in each of the triangles, we can see that there is a pattern. The numbers of dots increase by (n+1) adding 2, 3, 4 and 5. Therefore, this hints that the next three terms will be as we will be adding 6, 7, 8.

Next Three Terms

From the above triangular pattern, we can deduce a general statement which can represent the nth triangular number in terms of n. Butin order to do this, a table of n, Tn,1st difference and 2nd difference should be drawn:

From the above table, we can see that our variables are n and Tn. When we try to classify this pattern, we can see that it is not arithmetic. Arithmetic sequences require a common difference (d). Meaning that when we subtract

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