Isometric Sequences
- Decide on a pattern (you only need to do one set)
- You need to have 6 steps or more.
- I choose a Regular Hexagon for Position 1
- I made it grow, with an Equilateral Triangle from each side for Position 2
- For Positions 3 to 6, I grew these triangles.
- Position 1: 6 triangles
- Position 2: 12 triangles (add 6 to previous term)
- Position 3: 18 triangles (add 6 to previous term)
- Position 4: 24 triangles (add 6 to previous term)
- Position 5: 30 triangles (add 6 to previous term)
- Position 6: 36 triangles (add 6 to previous term)
For the nth rule, we look at the difference in the terms, in the above case it is add 6. We know that the coefficient of x (that is the number before x) is 6.
nth rule = 6x
The nth rule enables us to find out how many triangles there are in which ever position we choose.
If we look at position 6, we can calculate how many triangles we will need without drawing out the pattern.
nth rule = 6x, 6 x 6 = 36 triangles
- Position 1: 5 triangles
- Position 2: 9 triangles (add 4 to previous term)
- Position 3: 13 triangles (add 4 to previous term)
- Position 4: 17 triangles (add 4 to previous term)
- Position 5: 21 triangles (add 4 to previous term)
- Position 6: 25 triangles (add 4 to previous term)
For the nth rule, we look at the difference in the terms, in the above case it is add 4. We know that the coefficient of x (that is the number before x) is 6. However, if we substitute Position 1 into the rule, we get 4 x 1 = 4, but we need it to be 5! We need to add 1 to the rule to make it work
nth rule = 4x + 1
The nth rule enables us to find out how many triangles there are in which ever position we choose, whether it be Position 1, Position 6 or Position 6001!
If we look at position 6, we can calculate how many triangles we will need without drawing out the pattern.
nth rule = 4x, 4 x 6 + 1 = 25 triangles
