MIP1502
Assignment 3 2025
Unique number: 721003
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:
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By making use of this document you agree to:
Use this document
Fully accept the consequences
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comparison purposes,
Ensure originality of your own work, and fully accept the consequences should you plagiarise or misuse this document.
Comply with all relevant standards, guidelines, regulations, and legislation governing academic and written work.
Disclaimer
Great care has been taken in the preparation of this document; however, the contents are provided "as is" without any express or
implied representations or warranties. The author accepts no responsibility or liability for any actions taken based on the
information contained within this document. This document is intended solely for comparison, research, and reference purposes.
Reproduction, resale, or transmission of any part of this document, in any form or by any means, is strictly prohibited.
, +27 67 171 1739
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:
Disclaimer
Great care has been taken in the preparation of this document; however, the contents are provided "as is"
without any express or implied representations or warranties. The author accepts no responsibility or
liability for any actions taken based on the information contained within this document. This document is
intended solely for comparison, research, and reference purposes. Reproduction, resale, or transmission
of any part of this document, in any form or by any means, is strictly prohibited.
, +27 67 171 1739
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
1−0=1
Disclaimer
Great care has been taken in the preparation of this document; however, the contents are provided "as is"
without any express or implied representations or warranties. The author accepts no responsibility or
liability for any actions taken based on the information contained within this document. This document is
intended solely for comparison, research, and reference purposes. Reproduction, resale, or transmission
of any part of this document, in any form or by any means, is strictly prohibited.
Assignment 3 2025
Unique number: 721003
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:
Terms of use
By making use of this document you agree to:
Use this document as a guide for learning, comparison and reference purpose,
Terms of use
Not to duplicate, reproduce and/or misrepresent the contents of this document as your own work,
By making use of this document you agree to:
Use this document
Fully accept the consequences
solely as a guide forshould you plagiarise
learning, reference,or and
misuse this document.
comparison purposes,
Ensure originality of your own work, and fully accept the consequences should you plagiarise or misuse this document.
Comply with all relevant standards, guidelines, regulations, and legislation governing academic and written work.
Disclaimer
Great care has been taken in the preparation of this document; however, the contents are provided "as is" without any express or
implied representations or warranties. The author accepts no responsibility or liability for any actions taken based on the
information contained within this document. This document is intended solely for comparison, research, and reference purposes.
Reproduction, resale, or transmission of any part of this document, in any form or by any means, is strictly prohibited.
, +27 67 171 1739
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:
Disclaimer
Great care has been taken in the preparation of this document; however, the contents are provided "as is"
without any express or implied representations or warranties. The author accepts no responsibility or
liability for any actions taken based on the information contained within this document. This document is
intended solely for comparison, research, and reference purposes. Reproduction, resale, or transmission
of any part of this document, in any form or by any means, is strictly prohibited.
, +27 67 171 1739
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
1−0=1
Disclaimer
Great care has been taken in the preparation of this document; however, the contents are provided "as is"
without any express or implied representations or warranties. The author accepts no responsibility or
liability for any actions taken based on the information contained within this document. This document is
intended solely for comparison, research, and reference purposes. Reproduction, resale, or transmission
of any part of this document, in any form or by any means, is strictly prohibited.
