Geometric progression having the first and last values and the number of steps

Question

Here's the task at hand:

• I have the first and last values (a range from 0 to 100)
• I have the number of steps (20)
• I need to find values for all 20 steps

So, a simple arithmetic progression would be to use the difference of 5 for each step. However, I want the difference between steps 19-20 to be the biggest and the difference between steps 1-2 to be the smallest, with the rest of values progressively between the two.

What are my options? How do I go about solving this?

Answer 1

Ratio between successive terms in a progression with first value A, last value B and number of steps N is r = (B/A)^(1/N)