本题目来源于试卷: Sequences & Series，类别为 IB数学
[问答题]
The first two terms of an infinite ge41 mh b2l5(8 p)pqfut ogskpw1omet+ ihw(lcy+ n.4 i*vtrzric sequence, in order, are
$3 \log _{3} x, 2 \log _{3} x, \text { where } x>0 \text {. }$
1. Find the common ratio, r .
2. Show that the sum of the infinite sequence is $9 \log _{3} x$ .
The first three terms of an arithmetic sequence, in order, are
$\log _{3} x, \log _{3} \frac{x}{3}, \log _{3} \frac{x}{9}, \text { where } x>0$ .
3. Find the common difference d , giving your answer as an integer.
Let S_{6} be the sum of the first 6 terms of the arithmetic sequence. __
4. Show that $S_{6}=6 \log _{3} x-15$
5. Given that $S_{6}$ is equal to one third of the sum of the infinite geometric sequence, find x , giving your answer in the form $a^{p}$ where a, $p \in \mathbb{Z}$ .
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