本题目来源于试卷: Exponents & Logs，类别为 IB数学
[问答题]
The first three terms of aq: 7f9boc8m*u phdqc+ n ie9ppw+(p exzb-( j jld2h-3udnfinite sequence, in order, are $2 \ln x, q \ln x$,$ \ln \sqrt{x}$ where x>0 .
First consider the case in which the series is geometric.
1. 1. Find the possible values of q .
2. Hence or otherwise, show that the series is convergent.
2. Given that q>0 and $S_{\infty}=8 \ln 3$ , find the value of x .
Now suppose that the series is arithmetic.
3. 1. Show that $q=\frac{5}{4}$ .
2. Write down the common difference in the form $m \ln x$ , where $m \in \mathbb{Q}$ .
4. Given that the sum of the first n terms of the sequence is $\ln \sqrt{x^{5}}$ , find the value of n .
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