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What is the next term in the sequence below?
1/2, 2/6, 3/18, 4/54, ____
 one year ago
 one year ago
What is the next term in the sequence below? 1/2, 2/6, 3/18, 4/54, ____
 one year ago
 one year ago

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YorbelHunterBest ResponseYou've already chosen the best response.0
\[\frac{ 1 }{ 2 }, \frac{ 2 }{ 6 },\frac{ 3 }{ 18 },\frac{ 4 }{ 54 },\frac{ ? }{ ? }\]
 one year ago

YorbelHunterBest ResponseYou've already chosen the best response.0
1/2 + 1/3 + 1/6 + 1/9??
 one year ago

LolWolfBest ResponseYou've already chosen the best response.3
We note: \[ \frac{a_n}{b_n}=\frac{a_{n1}+1}{3b_{n1}} \]So: \[ \frac{5}{162} \]Is our next term.
 one year ago

mathsloverBest ResponseYou've already chosen the best response.0
Arithmetic Progression : try to check whether there is common difference or not ... \[\large{\frac{2}{6}\frac{1}{2} = \frac{23}{6}=\frac{1}{6}=d}\] \[\large{\frac{3}{18}\frac{2}{6}=\frac{36}{18}=\frac{3}{18}=\frac{1}{6}=d}\] hence the above sequence is of arithmetic progression
 one year ago

mathsloverBest ResponseYou've already chosen the best response.0
\[\large{\frac{4}{54}+\frac{1}{6}= \frac{49}{54}=\frac{5}{54}}\]
 one year ago

LolWolfBest ResponseYou've already chosen the best response.3
It's not an arithmetic series @mathslover , since: \[ \lim_{n\to\infty}\left(\frac{a_n}{b_n}\right)=0 \]
 one year ago

mathsloverBest ResponseYou've already chosen the best response.0
but it do have common difference...
 one year ago

LolWolfBest ResponseYou've already chosen the best response.3
For the first three terms, check: \[ \frac{4}{54}\frac{3}{18}\ne \frac{1}{6} \]
 one year ago
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