I want to divide a line segment which is of a fixed length, in to multiple section, where each successive section is greater than preceding section in length by a particular factor 'a' where 'a > 1'.
There is a also a minimum and maximum limit on the length of the sections.
for example if I have a line segment of length 10, and I want to divide it in to sections
where minimum section length is 1 and maximum section length is 3.
so my question is that is there any way using which I can determine the number of sections 'n' which can probably give a close result to divide a the line with minimum length approximately equal to 1 and maximum length 3, and each section other than the first one is greater than the previous section by a factor a.