Suzma is training for a marathon. In the first week she runs \(10\text{ km}\). Then each week she runs a distance that is 10% greater than the week before.
The total distance that Suzma has run by the end of \(n\) whole weeks is more than \(200\text{ km}\). Find the smallest possible value of \(n\).[4]
A geometric progression has 1st term \(a\) and common ratio \(r\), where \(a\ne0\) and \(r\ne1\). The 1st, 2nd and 3rd terms of the geometric progression are the 1st, 3rd and 7th terms of an arithmetic progression. Find the value of \(r\).[4]
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