# What's the next number in this sequence? **URL:** \ **Category:** Factual Questions\ **Created:** [October 27, 2008, 8:47pm UTC](https://boards.straightdope.com/t/whats-the-next-number-in-this-sequence/469841 "2008-10-27T20:47:40Z")\ **Posts on this page:** 17\ **Page:** 1
**Author:** ![Dahu](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/dahu/32/3416_2.png) [@Dahu](https://boards.straightdope.com/u/Dahu)\ **Post date:** [October 27, 2008, 8:47pm UTC](https://boards.straightdope.com/t/whats-the-next-number-in-this-sequence/469841/1 "2008-10-27T20:47:40Z")
7 10 13 18 25 36 On a quiz I saw today. I’m sure it’s really obvious, but I just can’t work it out. I’ve got the answer… but still I can’t get it. Anyone help? ---
**Author:** ![ultrafilter](https://avatars.discourse-cdn.com/v4/letter/u/3d9bf3/32.png) [@ultrafilter](https://boards.straightdope.com/u/ultrafilter)\ **Post date:** [October 27, 2008, 8:56pm UTC](https://boards.straightdope.com/t/whats-the-next-number-in-this-sequence/469841/2 "2008-10-27T20:56:01Z")
Is the answer 49 or 53? ---
**Author:** ![friedo](https://avatars.discourse-cdn.com/v4/letter/f/8edcca/32.png) [@friedo](https://boards.straightdope.com/u/friedo)\ **Post date:** [October 27, 2008, 8:57pm UTC](https://boards.straightdope.com/t/whats-the-next-number-in-this-sequence/469841/3 "2008-10-27T20:57:06Z")
All I’ve got is that the intervals are all prime numbers: 7 + **3** = 10, 10 + **3** = 13, 13 + **5** = 18, 18 + **7** = 25, 25 + **11** = 36 ---
**Author:** ![brad\_d](https://avatars.discourse-cdn.com/v4/letter/b/50afbb/32.png) [@brad\_d](https://boards.straightdope.com/u/brad_d)\ **Post date:** [October 27, 2008, 8:58pm UTC](https://boards.straightdope.com/t/whats-the-next-number-in-this-sequence/469841/4 "2008-10-27T20:58:05Z")
It looks to me like: n[sub]1[/sub]=7 n[sub]2[/sub]=10 for k \>= 3: n[sub]k[/sub]=n[sub]k-2[/sub]+n[sub]k-1[/sub]-(k+1) IOW, each number is the sum of the previous two minus a value that increases by one for each term. 7 + 10 - 4 = 13 10 + 13 - 5 = 18 13 + 18 - 6 = 25 18 + 25 - 7 = 36 25 + 36 - 8 = 53 So… 53? ---
**Author:** ![Giles](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/giles/32/60_2.png) [@Giles](https://boards.straightdope.com/u/Giles)\ **Post date:** [October 27, 2008, 8:59pm UTC](https://boards.straightdope.com/t/whats-the-next-number-in-this-sequence/469841/5 "2008-10-27T20:59:15Z")
My guess is 51 – and that’s not arrived at by taking the mean of **ultrafilter** ’s answers. ---
**Author:** ![Kid\_A\_1](https://avatars.discourse-cdn.com/v4/letter/k/ed8c4c/32.png) [@Kid\_A\_1](https://boards.straightdope.com/u/Kid_A_1)\ **Post date:** [October 27, 2008, 9:01pm UTC](https://boards.straightdope.com/t/whats-the-next-number-in-this-sequence/469841/6 "2008-10-27T21:01:11Z")
7 + 10 = 17 - 4 = 13 10 + 13 = 23 - 5 = 18 13 + 18 = 31 - 6 = 25 18 + 25 = 43 - 7 = 36 25 + 36 = 61 - 8 = 53 ---
**Author:** ![Giles](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/giles/32/60_2.png) [@Giles](https://boards.straightdope.com/u/Giles)\ **Post date:** [October 27, 2008, 9:04pm UTC](https://boards.straightdope.com/t/whats-the-next-number-in-this-sequence/469841/7 "2008-10-27T21:04:39Z")
I should add that my justification was by taking first differences – 3,3,5,7,11 – then second differences – 0,2,2,4. The best way I saw to continue that pattern was a second 4, giving 15 as the next first difference, thus 36+15 = 51 as the next number. But with short samples like this you can usually generate multiple plausible answers. ---
**Author:** ![Quartz](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/quartz/32/267_2.png) [@Quartz](https://boards.straightdope.com/u/Quartz)\ **Post date:** [October 27, 2008, 9:13pm UTC](https://boards.straightdope.com/t/whats-the-next-number-in-this-sequence/469841/8 "2008-10-27T21:13:43Z")
I think **brad d** has it. ---
**Author:** ![Dahu](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/dahu/32/3416_2.png) [@Dahu](https://boards.straightdope.com/u/Dahu)\ **Post date:** [October 27, 2008, 9:17pm UTC](https://boards.straightdope.com/t/whats-the-next-number-in-this-sequence/469841/9 "2008-10-27T21:17:11Z")
Yes! 53 was the answer given. Can see it now. I can sleep easily tonight. Thanks all. ---
**Author:** ![Kyrie\_Eleison](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/kyrie_eleison/32/7682_2.png) [@Kyrie\_Eleison](https://boards.straightdope.com/u/Kyrie_Eleison)\ **Post date:** [October 27, 2008, 9:41pm UTC](https://boards.straightdope.com/t/whats-the-next-number-in-this-sequence/469841/10 "2008-10-27T21:41:05Z")
I think this is an alternative expression of **brad\_d** ’s solution: n[sub]0[/sub] = 7 n[sub]k[/sub] = n[sub]k-1[/sub] + 2F[sub]k[/sub] + 1, where F[sub]n[/sub] is the nth Fibonacci number. The Fibonacci pattern in the differences is what jumped out at me. ---
**Author:** ![Napier](https://avatars.discourse-cdn.com/v4/letter/n/ce73a5/32.png) [@Napier](https://boards.straightdope.com/u/Napier)\ **Post date:** [October 27, 2008, 10:09pm UTC](https://boards.straightdope.com/t/whats-the-next-number-in-this-sequence/469841/11 "2008-10-27T22:09:52Z")
In fairness, the next number could be anything. Somebody thought this a cute way to create a sequence, and Ultrafilter and BradD both apparently thought of that cute way or its equivalent. But there must be infinite different ways of creating any given sequence of any length, albeit perhaps messy. ---
**Author:** ![Chronos](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/chronos/32/134_2.png) [@Chronos](https://boards.straightdope.com/u/Chronos)\ **Post date:** [October 27, 2008, 11:32pm UTC](https://boards.straightdope.com/t/whats-the-next-number-in-this-sequence/469841/12 "2008-10-27T23:32:47Z")
> [@](#): > > But there must be infinite different ways of creating any given sequence of any length, albeit perhaps messy. If nothing else, you can come up with a polynomial which will pass through any given finite set of points. I could construct a polynomial which passes through the points (1,7) (2,10) (3,13) (4,18) (5,25) (6,36) (7,53) , but then again, I could also construct a polynomial which passes through the points (1,7) (2,10) (3,13) (4,18) (5,25) (6,36) (7,6973246892) ---
**Author:** ![KneadToKnow](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/kneadtoknow/32/3999_2.png) [@KneadToKnow](https://boards.straightdope.com/u/KneadToKnow)\ **Post date:** [October 27, 2008, 11:48pm UTC](https://boards.straightdope.com/t/whats-the-next-number-in-this-sequence/469841/13 "2008-10-27T23:48:49Z")
> [@Napier](#): > > In fairness, the next number could be anything. Somebody thought this a cute way to create a sequence, and Ultrafilter and BradD both apparently thought of that cute way or its equivalent. But there must be infinite different ways of creating any given sequence of any length, albeit perhaps messy. This is always my problem with “lateral thinking” puzzles that I see. I read the answer, and I say, “yes, that’s an answer; but until you can prove to me that’s the _only_ answer, then you haven’t helped me any.” “There’s a guy in a field with two empty shotgun shells and a fifth of ripple. He’s covered in acne and wearing an ‘I’m with stupid’ t-shirt. Where did he go to college?” _Pfft_. ---
**Author:** ![ultrafilter](https://avatars.discourse-cdn.com/v4/letter/u/3d9bf3/32.png) [@ultrafilter](https://boards.straightdope.com/u/ultrafilter)\ **Post date:** [October 27, 2008, 11:51pm UTC](https://boards.straightdope.com/t/whats-the-next-number-in-this-sequence/469841/14 "2008-10-27T23:51:39Z")
> [@KneadToKnow](#): > > “There’s a guy in a field with two empty shotgun shells and a fifth of ripple. He’s covered in acne and wearing an ‘I’m with stupid’ t-shirt. Where did he go to college?” Michigan. ---
**Author:** ![KneadToKnow](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/kneadtoknow/32/3999_2.png) [@KneadToKnow](https://boards.straightdope.com/u/KneadToKnow)\ **Post date:** [October 27, 2008, 11:52pm UTC](https://boards.straightdope.com/t/whats-the-next-number-in-this-sequence/469841/15 "2008-10-27T23:52:36Z")
Frakkin’ show-off. ---
**Author:** ![Contrapuntal](https://avatars.discourse-cdn.com/v4/letter/c/e274bd/32.png) [@Contrapuntal](https://boards.straightdope.com/u/Contrapuntal)\ **Post date:** [October 27, 2008, 11:54pm UTC](https://boards.straightdope.com/t/whats-the-next-number-in-this-sequence/469841/16 "2008-10-27T23:54:41Z")
> [@ultrafilter](#): > > Michigan. And then Carolina Law. ---
**Author:** ![KneadToKnow](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/kneadtoknow/32/3999_2.png) [@KneadToKnow](https://boards.straightdope.com/u/KneadToKnow)\ **Post date:** [October 27, 2008, 11:58pm UTC](https://boards.straightdope.com/t/whats-the-next-number-in-this-sequence/469841/17 "2008-10-27T23:58:32Z")
> [@Contrapuntal](#): > > And then Carolina Law. Explains the ripple.