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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1 Answer
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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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2$\begingroup$ 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 at 18:42
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$\begingroup$ @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 at 16:33