Best to set up a table of values and look for a pattern.
Look at stage 1 and compare to stage 2:
Can you see that in stage 2, 3 more triangles are removed, one on each side of the triangle removed in stage 1?
Now look and compare stage 2 to stage 3:
Again, for each of the triangles removed in stage 2, there are three more removed around it (ie 3x3 = 9) removed in stage 3
For stage 4, each of these 9 will have 3 removed from around it, ie 9x3 =27 removed.
The "triangles removed column" are powers of 3.
Note that the triangles removed = 3 ^ (stage number -1)
So, the number of triangles removed in stage 21 will be 3^20.
Stage number | triangles removed |
1 | 1 = 3^0 |
2 | 3 = 3^1 |
3 | 9 = 3^2 |
4 | 27 = 3^3 |