Make a list that the next number is always the previous values plus half of the previous number

Hi everyone! I would like to make a list that the next value is always the previous values plus half of the previous number. If i have 20 the following value is 20 + 10 = 30; the next 20 + 10 + 5 = 35; the next 20 + 10 + 5 + 2.5 = 37.5 . Making a list like the one i did manually in the image. I would also like to be able to assign a minimum value to the or a maximum amount of values.
I upload an image
Would someone know how to solve it?
Thank you in advance :grinning:

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Thank you so much!