Question

A sequence of patterns is made from circular tiles and square tiles. Here are the first three patterns in the sequence: a) How many square tiles are needed to make Pattern Number 7? [2 MARKS] b) How many circular tiles are needed to make Pattern Number 20? [2 MARKS] c) When the pattern number is odd, the total number of tiles (SQUARE & CIRCULAR) needed to make the pattern: A - will always be even | B - will always be odd | C - could be even or odd | [2 MARKS] !! PLEASE ANSWER ALL OF THE QUESTIONS !!

Answer 1

The patterns of tiles do not follow an arithmetic sequence or geometric sequence

When the pattern number is odd, the total number of tiles (SQUARE & CIRCULAR) needed to make the pattern will always be odd

The square tiles needed to make Pattern Number 7?

From the question, we have the following pattern:

• Pattern 1: 1 square and 8 circles
• Pattern 2: 4 squares and 12 circles
• Pattern 3: 9 squares and 16 circles

The number of square tiles is calculated using:

Tn= n²

So, we have:

T₇ = 7²

T₇ = 49

Hence, 49 square tiles are needed in pattern 7

The circular tiles needed to make Pattern Number 20

The number of circular tiles is calculated using:

Tn= 4n + 4

So, we have:

T₂₀= 4 * 20 + 4

T₂₀= 84

Hence, 84 circular tiles are needed in pattern 20

c) The conclusion on odd pattern number

Using the computations in (a) and (b), we have:

The total number of tiles in odd pattern number is always odd

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