Missing arrangements question

[Rsimpson22]

I’m having trouble figuring out the pattern of what goes third. I’m assuming it would be 4 triangle but i can’t see the pattern.

 

[Dr.Peterson]

I have to say, I'm confused too. If we put 4 triangles there, then the number of triangles will be multiplied successively by 2, 2, 2, and then 4, which doesn't feel right; and the overall shapes might be triangle, rhombus, triangle, rhombus, rhombus. "Patterns" sometimes can't be recognized until they are explained by their maker! (And I wouldn't be very surprised to learn that this is a mistake.)

I sometimes wish curriculum writers didn't think this was math, because it isn't. It's guessing.

 

[kongzi]

We can try the following that looks consistent for me :

Consider these shapes as a sequence Shape_n starting from n=0

Shape_n= Regular shape formed of 2ⁿ of Shape₀

In this case Shape₂ =

 

[Dr.Peterson]

We can try the following that looks consistent for me :

Consider these shapes as a sequence Shape_n starting from n=0

Shape_n= Regular shape formed of 2ⁿ of Shape₀

In this case Shape₂ = View attachment 18120

I could quibble about the word "regular"; but the important thing is that you're saying that the last shape, Shape₄, should have 2⁴ = 16 little triangles. Does it? No!

As I pointed out, the number of little triangles is not doubled each time.