Assignment 4: Compulsory
Contributes 25% to the final pass mark
Unique number: 397869
Due date: 16 August 2024
, Question 1
1.1.1
Tile number (n) 5 6
Tile length (l) 7 8
Number of red squares (𝑅) 12 14
Number of black squares 37 50
(𝐵)
Total number of squares 49 64
(𝑆)
1.1.2
The pattern shows that the total number of squares (S) for any tile number (n) is equal
to the square of the tile length (l).
Therefore, the tile length (l) increases by 1 as the tile number (n) increases by 1.
So, for tile number 7:
l=n+2=7+2=9
1.1.3.1
Rn = 2n + 2 where n is the tile number.
Given l = n + 2, it can be rewritten as Rn in terms of l:
R = 2 (L−2) + 2 = 2L−4.
1.1.3.2
Given that the sequence of black squares follows a quadratic pattern,
Contributes 25% to the final pass mark
Unique number: 397869
Due date: 16 August 2024
, Question 1
1.1.1
Tile number (n) 5 6
Tile length (l) 7 8
Number of red squares (𝑅) 12 14
Number of black squares 37 50
(𝐵)
Total number of squares 49 64
(𝑆)
1.1.2
The pattern shows that the total number of squares (S) for any tile number (n) is equal
to the square of the tile length (l).
Therefore, the tile length (l) increases by 1 as the tile number (n) increases by 1.
So, for tile number 7:
l=n+2=7+2=9
1.1.3.1
Rn = 2n + 2 where n is the tile number.
Given l = n + 2, it can be rewritten as Rn in terms of l:
R = 2 (L−2) + 2 = 2L−4.
1.1.3.2
Given that the sequence of black squares follows a quadratic pattern,
