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

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

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.01/2 + 1/3 + 1/6 + 1/9??

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0We note: \[ \frac{a_n}{b_n}=\frac{a_{n1}+1}{3b_{n1}} \]So: \[ \frac{5}{162} \]Is our next term.

mathslover
 4 years ago
Best ResponseYou've already chosen the best response.0Arithmetic 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

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

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

mathslover
 4 years ago
Best ResponseYou've already chosen the best response.0but it do have common difference...

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0For the first three terms, check: \[ \frac{4}{54}\frac{3}{18}\ne \frac{1}{6} \]
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