POW 9 solutions...

Today we went over different solutions to POW9.

The formula to calculate the height of the tallest platform:
ht = hi + d(n-1), where "ht" is the height of the tallest, "hi" is the height of the initial platform, "d" is the difference in height between the platforms, "n" is the total number of platforms.
Can you explain how this formula works?

One method to find the amount of fabric need for all of the platforms is to add up the height of each platform.

Fabric = hi + [hi + 1d] + [hi + 2d] + [hi + 3d] + ... + [hi + (n-1)d]
Notice that the last term, hi + (n-1)d, is actually hf, the height of the final platform.

But some people mentioned that adding up all of the heights is not an instant way to get amount of fabric. Plus, you kind of need to know the number of platforms to figure out how many times you have to add the numbers.

One formula that we could use to instantly calculate the amount of fabric need for all of the platforms:
Fabric = n(hi + hf)/2
Can you explain how this formula works?

See 3 very good examples of my POW journaling expectations. Example 1. Example 2. Example 3.