Hello! Need help to help my daughter! I have attached a picture of the question. We know the answer. Just not how to solve.

[Hharouff]

 

[Harry_the_cat]

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

 

[Hharouff]

Thank you!

 

[Dr.Peterson]

Your answer is 3^20, the number removed at the 21st stage. What you are asked for is the total number removed through the 21st stage.

Do you know the sum of a geometric series?

 

[Hharouff]

 

[Hharouff]

We solved. Thank you. She was forgetting to divide by 2! Thank you everyone for your help!