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The sequence (from my child's "for fun" challenge packet, not for credit or graded) is:

4,4,2,6,2,10,4,_

The possible answers are:

  • A) 15
  • B) 20
  • C) 25
  • D) 28
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    $\begingroup$ 2) jmcarson sure has an impressive beard for a 4th grader. :^) $\endgroup$
    – DanDan面
    Commented Apr 25 at 3:02
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    $\begingroup$ I am the parent. It is a “for fun” challenge packet, not for credit or graded or anything :) $\endgroup$
    – jmcarson
    Commented Apr 25 at 3:18
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    $\begingroup$ Welcome to PSE (Puzzling Stack Exchange)! $\endgroup$ Commented Apr 25 at 9:40
  • $\begingroup$ Is this US 4th grade, meaning the kid is 6+4=10 yo? If so this is an impressive "for fun" assignement. $\endgroup$
    – WoJ
    Commented Apr 27 at 5:31

2 Answers 2

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I think the answer is

D) 28

Reason

With the original sequence if you divide each odd term with its next adjacent even term you get 1/1 (4/4), 1/3 (2/6), 1/5 (2/10) where the denominator increases by 2 each time and so 28 is the answer as it is the only one that makes 4/28 which is 1/7, fitting in the pattern established. You could conversely divide each even term with the odd term before it making 1,3,5,7 from another perspective.

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    $\begingroup$ Thank you! Really appreciate the clear explanation. $\endgroup$
    – jmcarson
    Commented Apr 25 at 3:50
  • $\begingroup$ I don't think denominator increases by 2 each time edit: nvm i get it now $\endgroup$
    – Sny
    Commented Apr 25 at 11:23
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Same answer as PDT, just explained differently:

enter image description here

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    $\begingroup$ this is a better explanation of what is going on! I just stopped thinking about the sequence once I spotted the division pattern. Nice spot though! +1 $\endgroup$
    – PDT
    Commented Apr 25 at 9:56
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    $\begingroup$ @PDT: Better is in the eye of the beholder. It's always bugged me that for the sequences puzzles there's always many different explanations, and while the "simpler" is likely "better", guessing what the asker might have thought of is such an open-ended question :'( $\endgroup$ Commented Apr 25 at 10:18
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    $\begingroup$ I'd actually go so far as to say this should be the accepted answer. If @PDT's explanation was all there was to it, the ninth number could really be anything. Also, this exhibits the underlying 1,2,3,... sequence. (No offense!) $\endgroup$
    – Oliphaunt
    Commented Apr 25 at 19:18
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    $\begingroup$ @Stiv Thanks! I was surprised and pleased to get a gold badge; I know they are rarely awarded. $\endgroup$ Commented Apr 26 at 16:55
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    $\begingroup$ Fun fact (not for 4th graders): suppose we change the first term from $4$ to $x$. Then if $x > 1 + \sqrt{2\pi e} \operatorname{erf}(\frac{\sqrt2}{2})$, the sequence diverges to $+\infty$, and if $x < 1 + \sqrt{2\pi e} \operatorname{erf}(\frac{\sqrt2}{2})$, the sequence diverges to $-\infty$. (This threshold is approximately $3.82137$.) $\endgroup$ Commented Apr 27 at 22:28

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