Find the next number.

[jjane]

7, 4, 10, 26, 53, 92, 144,____

please explain how you arrived at your answer.

[Puck]

Sorry, OEIS says that those numbers don't exist in that order.

[tricky77puzzle]

Sorry, OEIS says that those numbers don't exist in that order.

Then the whole point is to try and find that order that they belong in.

Let's see, 7, 4, 10...

Might it be some quadratic function?

There's also:

Spoiler:

7 + 4 - 1 = 10
4 + 10 + 12 = 26
26 + 26 + 1 = 53
26 + 53 + 23 = 92
53 + 92 - 1 = 144

So maybe 92 + 144 + 34 is the next term, or 270.

[++$_]

I know what the next number is. I obtained my answer using finite differences.

Is this a homework problem?

[Ratio]

Show our workings? You're making us do your homework? Tsk Tsk!

[Lycur]

4 + 10 + 10 = 26

O RLY?

[tricky77puzzle]

4 + 10 + 10 = 26

O RLY?

okay, damn. I, uh... mae a miscalculation.

[thc]

Spoiler:

The answer is 210. Take differences between terms.

[tricky77puzzle]

Spoiler:

The answer is 210. Take differences between terms.

Uh huh. That's a very big spoiler. Thanks a lot... so It was a quadratic function!

[++$_]

Spoiler:

The answer is 210. Take differences between terms.

Uh huh. That's a very big spoiler. Thanks a lot... so It was a quadratic function!

Spoiler:

Looks more like a cubic to me, but that's the answer I got as well.

[tricky77puzzle]

Spoiler:

The answer is 210. Take differences between terms.

Uh huh. That's a very big spoiler. Thanks a lot... so It was a quadratic function!

Spoiler:

Looks more like a cubic to me, but that's the answer I got as well.

If it were cubic, it wouldn't go down, then up, unless it were a cubic plus some linear term.

The reason it's... oh, wait, yes, it is a cubic. I am dumb...

[fransisco4]

I don't get it. Care to explain?

[douglasm]

I don't get it. Care to explain?

Spoiler:

Take the difference between each consecutive number in the sequence. You get -3, 6, 16, 27, 39, 52. Now do it again with that sequence to get 9, 10, 11, 12, 13. The pattern there should be rather obvious. 52+14 = 66, so the next term in the original sequence is 144+66 = 210.

[qinwamascot]

It really could be anything. There's no way to know what formula we're talking about from finitely many terms. The cubic one may seem simpler, but that doesn't make it any more correct.

the right answer is, of course, 42

[tricky77puzzle]

It really could be anything. There's no way to know what formula we're talking about from finitely many terms. The cubic one may seem simpler, but that doesn't make it any more correct.

the right answer is, of course, 42

Really, it could be anything.

I could define f(x) as the function that returns:

f(x|x<1) = f(x + 1) - 2(f(x + 2))
f(1) = 7
f(2) = 4
f(3) = 10
f(4) = 26
f(5) = 53
f(6) = 92
f(7) = 144
f(8) = 42
f(x|x>8) = 42

[Office_Shredder]

I'm pretty sure this discussion was already held

[jestingrabbit]

I'm pretty sure this discussion was already held

Yeah. It was in maths. Gotta say I side with Token on this one.

It irritates me that this sort of question frequently appears on 11+ tests and GCSE Maths exams. The next term could be any number at all, yet only one specific number is marked as correct.

It irritates ME that people think "it could be anything" is a clever answer.

[jjane]

for the record, it wasn't my homework. i'm not even in school right now.


(it was my MOM's homework)


thanks, dudes.

[ARP]

{7, 4, 10, 26, 53, 92, 144, 210, 291, 388, 502, 634, 785, 956, 1148, 1362, 1599, 1860, 2146, 2458, 2797, 3164, 3560, 3986, 4443, 4932, 5454, 6010, 6601, 7228, 7892, 8594}

a(n)=1/6*(108 - 88*n + 21*n^2 + n^3)