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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, ...
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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anonymous
 one year ago
Best ResponseYou've already chosen the best response.0well.... what's "r" or the common ratio? or what makes a geometric sequence a geometric sequence?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Umm.. what it is multiplied by? Isn't it like squares or something... I'm sorry I'm really bad at this stuff :(

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0let 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?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0yeap... so... notice \(\begin{array}{llll} term&value \\\hline\\ a_1&11\\ a_2&a_1\cdot r\implies 11\cdot 2\implies 22 \end{array}\qquad meaning\qquad a_2=a_1\cdot r\qquad thus \\ \quad \\\\ \quad \\ \cfrac{a_2}{a_1}=r\qquad or\qquad \cfrac{\cancel{22}}{\cancel{11}}=r\implies 2=r\)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0so.. to find "r", simply divide the "following term" by the term behind it :)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Oh! Awesome that is much easier than I thought thank you so much!

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0to find the 9th term, well \(\bf \large a_{\color{brown}{ n}}=a_1\cdot r^{{\color{brown}{ n}}1}\qquad \qquad a_{\color{brown}{ 9}}=a_1\cdot r^{{\color{brown}{ 9}}1}\)
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