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YorbelHunter

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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  1. YorbelHunter
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    \[\frac{ 1 }{ 2 }, \frac{ 2 }{ 6 },\frac{ 3 }{ 18 },\frac{ 4 }{ 54 },\frac{ ? }{ ? }\]

    • one year ago
  2. YorbelHunter
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    1/2 + 1/3 + 1/6 + 1/9??

    • one year ago
  3. LolWolf
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    We note: \[ \frac{a_n}{b_n}=\frac{a_{n-1}+1}{3b_{n-1}} \]So: \[ \frac{5}{162} \]Is our next term.

    • one year ago
  4. mathslover
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    Arithmetic Progression : try to check whether there is common difference or not ... \[\large{\frac{2}{6}-\frac{1}{2} = \frac{2-3}{6}=\frac{-1}{6}=d}\] \[\large{\frac{3}{18}-\frac{2}{6}=\frac{3-6}{18}=\frac{-3}{18}=\frac{-1}{6}=d}\] hence the above sequence is of arithmetic progression

    • one year ago
  5. mathslover
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    \[\large{\frac{4}{54}+\frac{-1}{6}= \frac{4-9}{54}=\frac{-5}{54}}\]

    • one year ago
  6. LolWolf
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    It's not an arithmetic series @mathslover , since: \[ \lim_{n\to\infty}\left(\frac{a_n}{b_n}\right)=0 \]

    • one year ago
  7. mathslover
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    but it do have common difference...

    • one year ago
  8. LolWolf
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    For the first three terms, check: \[ \frac{4}{54}-\frac{3}{18}\ne -\frac{1}{6} \]

    • one year ago
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