Nth Term Investigation

Authors Avatar

Introduction

In this bit of coursework I will draw shapes that tessellate and work on the parts in between them, I will look for patterns and will try to find the nth term, write a table of my results and draw line graphs as another way of showing my results.

Squares

I will firstly be looking at squares.

Here is a table showing my results:

For the second column  (  ) each square has 4 because the symbol represents the corners and all squares have 4 corners. The nth term is n= 4

For the third column    (   ) the amount goes up in 4’s because an extra symbol is needed 1 more time on each of the sides and there is 4 sides. The nth term for this is (n-1) x4.  

For the fourth column the numbers are square numbers because in the middle where these (+) are found they are in a formation of a square 2 by 2, 3 by 3 etc so you times them and they are square numbers. The nth for this one is (n-1)2.

Here are my predictions for other squares with different lengths.

Rectangles No.1

I will now move on to rectangles, as there are so many ways of doing rectangles I will start with one side going up by one each time (x) and the other side always being the same (t) which will be 2.

Here is a table showing my results:

For the second column  (  ) each rectangle has 4 because the symbol represents the corners and all rectangles have 4 corners. The nth term is n= 4

For the third column  (    ) the amount goes up in 2’s because the length increases by one and an extra T-shape symbol has toe be added to both sides. The nth term is n x t / n x 2.

For the fourth column (+) the numbers go up in 1’s because when the length increase by one an extra + is put in the middle of the rectangle. The nth term is n-1.

Join now!

Here are my predictions for other rectangles with different lengths.

Rectangles No.2

I will now do the same as the first lot of rectangles but instead of (t) being 2 it will be 3.

Here is a table showing my results:

For the second column (   ) each rectangle has 4 because the symbol represents the corners and all rectangles have 4 corners. The nth term is n= 4

For the third column (     ) the numbers go up in 2’s because the length ...

This is a preview of the whole essay