Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

Let's say I have this series of numbers 2, 5, 10, 17. Now somebody told me that next number is 26. He used this function for that:

f(n) = n*n + 1

Can anyone explain how does that function solve the problem to come up with 26?

share|improve this question
Look them up on the OEIS. These types of puzzles are pointless, especially when their solutions are non-mathematical. –  Qiaochu Yuan Nov 7 '10 at 12:55
This type of puzzle is never mathematical. –  anon Nov 7 '10 at 12:56
For OEIS, see research.att.com/njas/sequences . By definition, no matter how the sequence begins, the following numbers can be arbitrary. –  Jaska Nov 7 '10 at 13:07
@muad: that's not entirely true. Here is my favorite such problem, which has a totally mathematical solution, but is (in my opinion) impossible to guess unless you've seen it before: 1, infinity, 5, 6, 3, 3, ? –  Qiaochu Yuan Nov 7 '10 at 13:20
@Qiaochu: haven't seen it, but regular solids? –  Ross Millikan Nov 7 '10 at 14:52

3 Answers 3

up vote 7 down vote accepted

In general given any length $n$ sequence of numbers there exists a polynomial $p(x)$ of degree $n$ which gives this sequence. It's easy to find such a polynomial so I will not discuss how to do this. Note that as a consequence of this, if we are given a length $n$ sequence we can find a polynomial for the length $n+1$ sequence which gives any value we want after giving the values in the initial sequence.

Futhermore, there are many different types of function other than polynomials - many of which can fit any given sequence. For this reason it is impossible to really be "right" when answering a question of the form "What's the next number ...?". Any prediction is just as (in)valid without putting some constraints on it.

share|improve this answer
"What's the next number ...?". Any prediction is just as (in)valid without putting some constraints on it. I usually face more than one question in my aptitude module just like this .. and they hope for a correct answer!? :( –  Quixotic Nov 7 '10 at 14:02
@Debanjan, yes you just have to humor these people. –  anon Nov 7 '10 at 14:42

Take the position of the number. First is 1, second is 2 and so on.

So we have

$$ 1\cdot 1+1 = 2,\\ 2\cdot 2+1 = 5, \\ 3\cdot 3+1 = 10, \\ 4\cdot 4+1 = 17, \\ 5 \cdot 5+1 = 26$$

The tenth number in the sequence would be $$10\cdot 10+1 = 101.$$

share|improve this answer

It just goes like by just lookin at the question i get to know that the number is increasing which means something is being added. the number next to 2 is 5 which means 2+3=5 Now, by trying 5+3 i get 8 but the number coming up is 10 and we know that adding 5 to 5 will give me 10 so I concluded, skip and add the number 2+3=5 5+5(skipping 4) =10 now next to 5 comes 6 which we have to skip 10+7=17 17+9= 26. which is the answer. It took less than a minute figuring it out :) hope it helps

share|improve this answer
I think this should be re-written to be less chatty, as it is very confusing. –  Simon Hayward Nov 26 '12 at 10:01
I thought the answer was amusing –  tacos_tacos_tacos Dec 5 '12 at 7:36

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.