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

#### Harry_the_cat

##### Senior Member
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

Thank you!

#### Dr.Peterson

##### Elite Member
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

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