MIP1502 Assignment 3 (721003) |COMPLETE ANSWERS| - Due 18 July 2025

MIP1502
Assignment 3

Unique No: 721003
Due 18 July 2025

, ASSIGNMENT 3

UNIQUE NO: 721003

Question 1.1

Completed Table (Diagrams 1–10)

Diagram 1 2 3 4 5 6 7 8 9 10

Small triangles 1 4 9 16 25 36 49 64 81 100

Black triangles 1 3 5 7 9 11 13 15 17 19

Grey triangles 0 1 3 6 10 15 21 28 36 45

White triangles 0 0 1 3 6 10 15




1.1.1 Analyse the patterns (4 marks)

1.1.1.1 First Differences:

• Small triangles:
4–1=3
9–4=5
16 – 9 = 7
25 – 16 = 9
36 – 25 = 11
First differences: 3, 5, 7, 9, 11 (increasing) → Second differences: constant

• Black triangles:
3–1=2
5–3=2
7–5=2
9–7=2

, 11 – 9 = 2
First differences: 2 (constant)

• Grey triangles:
1–0=1
3–1=2
6–3=3
10 – 6 = 4
First differences: 1, 2, 3, 4 → Second differences: constant

• White triangles:
0–0=0
1–0=1
3–1=2
6–3=3
10 – 6 = 4
First differences: 0, 1, 2, 3, 4 → Second differences: constant

1.1.1.2 Classification:

• Small triangles: Quadratic

• Black triangles: Linear

• Grey triangles: Quadratic

• White triangles: Quadratic

1.1.1.3 Justification:

• The 'Black triangles' pattern is linear because its first differences are constant
(+2). A constant first difference is the key feature of a linear sequence.

• The 'Small triangles' pattern is quadratic because the first differences (3, 5, 7,
9…) increase by a constant amount. This means the second differences are
constant, which is the defining feature of a quadratic sequence.

1.1.2.1 Pattern Descriptions (2 marks)