MIP1502Assignment 3 2025
Unique Number:
Due date: 18 July 2025
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:
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replacement for individual research, critical analysis, or professional consultation. Students are encouraged to perform
their own research and seek advice from their instructors or academic advisors for specific assignment guidelines.
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assignments.
Academic Integrity: It is essential for students to maintain academic integrity and follow their institution's policies
regarding plagiarism, citation, and referencing. These study notes should be used as learning tools and sources of
inspiration. Any direct reproduction of the content without proper citation and acknowledgment may be considered
academic misconduct.
Limited Liability: The seller shall not be liable for any direct or indirect damages, losses, or consequences arising from
the use of these notes. This includes, but is not limited to, poor academic performance, penalties, or any other negative
consequences resulting from the application or misuse of the information provided.
, For additional support +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:
, For additional support +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
Unique Number:
Due date: 18 July 2025
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:
DISCLAIMER & TERMS OF USE
Educational Aid: These study notes are intended to be used as educational resources and should not be seen as a
replacement for individual research, critical analysis, or professional consultation. Students are encouraged to perform
their own research and seek advice from their instructors or academic advisors for specific assignment guidelines.
Personal Responsibility: While every effort has been made to ensure the accuracy and reliability of the information in
these study notes, the seller does not guarantee the completeness or correctness of all content. The buyer is
responsible for verifying the accuracy of the information and exercising their own judgment when applying it to their
assignments.
Academic Integrity: It is essential for students to maintain academic integrity and follow their institution's policies
regarding plagiarism, citation, and referencing. These study notes should be used as learning tools and sources of
inspiration. Any direct reproduction of the content without proper citation and acknowledgment may be considered
academic misconduct.
Limited Liability: The seller shall not be liable for any direct or indirect damages, losses, or consequences arising from
the use of these notes. This includes, but is not limited to, poor academic performance, penalties, or any other negative
consequences resulting from the application or misuse of the information provided.
, For additional support +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:
, For additional support +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
