Question

Large rectangular patterns are designed using small square tiles that contain circles, stars, and

triangles. Designs 1, 2, and 3 in this pattern are shown.
If this pattern continues, which expressions represent the number of each type of tile for
design n?
number of tiles with circles
number of tiles with stars
number of tiles with triangles
total number of tiles
[Choose]
[Choose]
[Choose
[Choose ]
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Answer 1

The correct answer is option b. 3 + 3(n-1) = 3n.

Based on the image, the number of triangles in each design follows an arithmetic sequence.

• Design 1 has 6 triangles.
• Design 2 has 9 triangles (6 triangles from Design 1 + 3 more triangles).
• Design 3 has 12 triangles (9 triangles from Design 2 + 3 more triangles).

Therefore, the number of triangles for design n can be represented by the following expression:

• 6 + 3(n - 1)

This expression matches option b. 3 + 3(n-1) = 3n.

The question probable maybe:

Large rectangular patterns are designed using small square tiles that contain circles, stars, and triangles. Designs 1, 2, and 3 in this pattern are shown. If this pattern continues, which expression represent the number of triangles for design n?

a. 6 + 2(n-1) = 2n + 4

b. 3 + 3(n-1) = 3n

c. 6

d. 6n