Exponents & Logs (id: c1d7b99c6)

本题目来源于试卷:  Exponents & Logs，类别为 IB数学

[填空题]
The first two terms of an mt wm mrn. t+*1vo68bsinfinite geometric sevx 2 j)62gae,n9g zozvquence, 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 .$a \log _{b} x$ a =    b =   

The first three terms of an arithmetic sequence, in order, are

$\log _{3} x, \log _{3} \frac{x}{3}, \log _{3} \frac{x}{9}, \text { where } x>0 \text {. }$

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 $S_{6}=6$ $\log _{3} x-15$ .$a \log _{b} x-c$ a =    b =    c =   
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, $p \in \mathbb{Z}$ .$a^b$a =    b =   

参考答案:
空格1: 2/3  空格2: 9  空格3: 3  空格4: -1  空格5: 6  空格6: 3  空格7: 15  空格8: 3  空格9: 5 


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