How to divide a given range of numbers into a series with an equal percentage increase for each share?

Question

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There is a given range from the bottom to the top number, let's say 34 - 54. There is a given number of shares of the range, let's say 21. You need to divide the range so that the growth of each share is an equal number of percent.
I understand how to divide the range into equal parts - we divide the entire range (in this case 54-34 = 20) into the required number of shares (20 / (21-1) = 1) and increment each part in a cycle this weight: 34, 35, 36 ... 53, 54. But at the same time, there will be a different percentage between the shares: at the bottom of the range 35/34*100-100 = 2.94%, and at the top of the range 54/53*100-100 = 1.89%. Is there a formula to get a series of a given number of shares with an equal growth percentage between them?

Answer 1

Have you heard of geometric progression?