Next number in the sequence -2 3 27 69 129 .. [closed]

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I was asked this on an aptitude test recently

Determine the next number in the sequence: $-2, 3, 27, 69, 129, \ ..$
A: $178$
B: $207$
C: $288$
D: $312$

I've been racking my brain for a few days trying to find the solution but I can't figure it out.

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3 Answers

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The next number would be 207. Look into the differences between terms 5, 24, 42, 60 And the difference between these is 19, 18, 18, So i thought the first 19 should be 18 also i. e. Our sequence will be -3, 3, 27, 69, 129, 207, ...

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It is $207$ and the OP made a typo The original sequence is

$-3, 3, 27, 69, 129, 207,\ldots$

$a_n=3 (3 - 7 n + 3 n^2)$ for any $n\in\mathbb{N}\land n\geq 1$

Hope this helps

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I think most smart comments agree that there is no real mathematical progression to be discovered here. Unless you may assume typos

So either this is an aptitude test on how you would solve impossible problems (being able to quickly acknowledge you don't know and able to tell why),

or this could be some tricky calculation where you'd have to transcribe the numbers and count the values of letters and add and/or multiply values, which probably is only valid in the mind of the developer of the test

or this is an aptitude test where the developer of the test failed. Sort of a special case of the previous case.

-- note: I love the '207' answers that make my answer look stupid ;) I'll +1 them. The approach is quite typical for such problems, and the assumption of a typo should be a question but is valid.

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