MIP1502 Assignment 3 (DETAILED ANSWERS) 2025 - DISTINCTION GUARANTEED

MIP1502
Assignment 3 2025
Unique #:

Due Date: 18 July 2025

Detailed solutions, explanations, workings
and references.

+27 81 278 3372

, QUESTION 1

Completed Table

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 21 28 36




1.1.1.1 Determine the first differences between consecutive terms

We calculate the first differences for each row in the table from Diagram 1 to
Diagram 10:

a) Small triangles:

Values: 1, 4, 9, 16, 25, 36, 49, 64, 81, 100
First differences:
4−1=3
9−4=5
16 − 9 = 7
25 − 16 = 9
36 − 25 = 11
49 − 36 = 13
64 − 49 = 15
81 − 64 = 17
100 − 81 = 19

→ First differences: 3, 5, 7, 9, 11, 13, 15, 17, 19

b) Black triangles:




Varsity Cube 2025 +27 81 278 3372

, Values: 1, 3, 5, 7, 9, 11, 13, 15, 17, 19
First differences:
3−1=2
5−3=2
7−5=2
9−7=2
11 − 9 = 2
13 − 11 = 2
15 − 13 = 2
17 − 15 = 2
19 − 17 = 2

→ First differences: 2, 2, 2, 2, 2, 2, 2, 2, 2

c) Grey triangles:

Values: 0, 1, 3, 6, 10, 15, 21, 28, 36, 45
First differences:
1−0=1
3−1=2
6−3=3
10 − 6 = 4
15 − 10 = 5
21 − 15 = 6
28 − 21 = 7
36 − 28 = 8
45 − 36 = 9

→ First differences: 1, 2, 3, 4, 5, 6, 7, 8, 9

d) White triangles:

Values: 0, 0, 1, 3, 6, 10, 15, 21, 28, 36
First differences:
0−0=0



Varsity Cube 2025 +27 81 278 3372