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What's the next term in the sequence?

$12$, $28$, $36$, $84$, $88$, $168$, $\ldots$

The possible choices are:

$174$, $170{2\over3}$, $188$, $169{1\over3}$, $176$

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  • $\begingroup$ Hi, and welcome to Puzzling :) Please can you supply a source for this question? All puzzles posted from elsewhere (e.g. puzzle books, newspapers, webpages, IQ tests, interview materials, etc.) need to have their original source mentioned in the post, so that credit can be given to the original creator(s). You can just edit the question to add a line explaining where you found it. Thanks! $\endgroup$
    – Stiv
    Jul 22, 2023 at 21:32

1 Answer 1

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Next term is:

$176$

Explanation:

The first term is $12$ (the first abundant number) and the next term is $28$ (the sum of the divisors of the first term). To get subsequent even-indexed terms, multiply the second term by successive triangular numbers ($3, 6, ...$). To get the following odd-indexed term, add the even-indexed term and its last digit. The seventh term is therefore $168+8=176$, the last option in your list of choices.

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    $\begingroup$ Your explanation of the sequence involves many things: Abundant numbers, sum of divisors, multiplication, triangle numbers, even/odd-indexed terms and adding the last digit. Typically sequence puzzles have simpler explanations. $\endgroup$ Jul 22, 2023 at 18:42
  • $\begingroup$ @WillOctagonGibson I think in theory if you remove the nonsense about the abundant numbers and sum of divisors and just assume 12 and 28 are magic constants, then the explanation provided makes a little more sense - but still very arbitrary. $\endgroup$ Jul 23, 2023 at 16:33

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