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

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.

## closed as off-topic by JMoravitz, mechanodroid, Henrik, kingW3, user296602 Oct 24 '17 at 19:14

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• What exactly have you tried? – StubbornAtom Oct 24 '17 at 18:01
• OEIS doesn't have anything. Where did you get this from? – Kaynex Oct 24 '17 at 18:02
• Define $$f(x) = 14 - \frac{329 x}{12} + \frac{287 x^2}{24} - \frac{7 x^3}{12} + \frac{x^4}{244}$$ Then $(-2,3,27,69,129) = (f(1),f(2),f(3),f(4),f(5))$. So naturally the next number is $f(6) = 208$ ;) – Clive Newstead Oct 24 '17 at 18:03
• The next number is $42$. You can't prove me wrong. But, at the same time you can't prove the person who says the next number is $43$ wrong either, or $44$ for that matter, or $\pi$ or $\sqrt{e-3.4}$ or anything else. There is simply not enough information to determine the next entry uniquely. – JMoravitz Oct 24 '17 at 18:06
• Then whoever wrote the test should be slapped across the face repeatedly unless they include an option for "not enough information" which is always the correct answer. Such questions are not well formed and do not have any way of answering. – JMoravitz Oct 24 '17 at 18:14

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, ...

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

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.