ACI2606 Assignment 4 (720960)|COMPLETE ANSWERS & SOLUTIONS|- Due 15 August 2025

ACI2606
Assignment 4

Unique No: 720960
Due 15 August 2025

, Assignment 4: Compulsory
Contributes 25% to the final pass mark
Unique number: 720960
Due date: 15 August 2025


Question 1

1.1

1.1.1 Complete the table.

From the pattern shown the purple tiles are: 2, 4, 6, ... (increase by 2 each size). White
tiles are: 0, 1, 2, ... (increase by 1 each size from size 1). Total = purple + white.

Size 𝑛 1 2 3 4 5 6 25

Purple 𝑃(𝑛) 2 4 6 8 10 12 50

White 𝑊(𝑛) 0 1 2 3 4 5 24

Total 𝑇(𝑛) 2 5 8 11 14 17 74

Working shown (sample calculations):

• For size 4: Purple = 6 + 2 = 8 . White = 3. Total = 8 + 3 = 11 .

• For size 25: Purple = 2 × 25 = 50 . White = 25 − 1 = 24 . Total = 50 + 24 = 74 .

1.1.2 Describe your methods in 1.1.1.

I looked at the change between successive sizes:

• Purple increases by 2 each size (2 → 4 → 6 → ...).

• White increases by 1 each size starting at 0 (0 → 1 → 2 → ...). So I used
arithmetic sequences and extended them to the requested sizes.

1.1.3 Rule for purple tiles.

𝑃(𝑛) = 2𝑛 . (Reason: at size 𝑛 there are two purple tiles per unit of size.)