## anonymous one year ago How do I solve this? What is the 9th term of this geometric sequence? 2/3, 2, 6, 18, 54, 162, ...

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1. jdoe0001

well.... what's "r" or the common ratio? or what makes a geometric sequence a geometric sequence?

2. anonymous

Umm.. what it is multiplied by? Isn't it like squares or something... I'm sorry I'm really bad at this stuff :(

3. jdoe0001

let us make a sequence lemme start with the 1st term say 11 and use the common ratio "r" of.. say 2 if 11 is the first term, what's the 2nd term?

4. anonymous

22?

5. jdoe0001

yeap... so... notice $$\begin{array}{llll} term&value \\\hline\\ a_1&11\\ a_2&a_1\cdot r\implies 11\cdot 2\implies 22 \end{array}\qquad meaning\qquad a_2=a_1\cdot r\qquad thus \\ \quad \\\\ \quad \\ \cfrac{a_2}{a_1}=r\qquad or\qquad \cfrac{\cancel{22}}{\cancel{11}}=r\implies 2=r$$

6. jdoe0001

so.. to find "r", simply divide the "following term" by the term behind it :)

7. anonymous

Oh! Awesome that is much easier than I thought thank you so much!

8. jdoe0001

to find the 9th term, well $$\bf \large a_{\color{brown}{ n}}=a_1\cdot r^{{\color{brown}{ n}}-1}\qquad \qquad a_{\color{brown}{ 9}}=a_1\cdot r^{{\color{brown}{ 9}}-1}$$

9. anonymous

so I got 4,374

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