2
$\begingroup$

I'm going to put in a series just to comply, but I was wondering if anyone had advice for figuring out patterns in numbers. All I hear is that some people are natural at it.

4, 6, 10, 18...

the context here is GED, so don't make answers too complicated.

Thanks

  • 10
    A standard trick is taking differences of neighboring numbers. In this case we get 2, 4, 8, which looks like the differences double each time. So the series could be $a_n = 2+2^n$.2011-09-18
  • 0
    Can I make a comment too complicated instead? What comes next in the sequence 0, 1, 2, 720! (that's 720 *factorial*), ? I think I first saw this in Hofstadter's *[Fluid Concepts and Creative Analogies](http://en.wikipedia.org/wiki/Fluid_Concepts_and_Creative_Analogies)*, but I'm not positive.2011-09-18
  • 0
    @Rahul: For $n\in\omega$ define $f_0(n)=n$ and $f_{k+1}(n)=f_k(n)!$. The $n$-th term of the sequence is then $f_n(n)$.2011-09-18
  • 1
    If people cannot find the pattern, then perhaps [computer can](http://oeis.org/search?q=4%2C+6%2C+10%2C+18&language=english&go=Search).2011-09-18
  • 3
    Next in the sequence 0,1,2,720! is 4!!!!. The rule is 0,1!,2!!,3!!!...2011-09-18
  • 0
    @Angela: Just a small observation: if you state it that way, you have to make $0$ a bit of a special case. The recursive definition that I used avoids that very minor irregularity but is otherwise identical.2011-09-18

1 Answers 1

0

Let's define recursive formula $a_n=a_{n-1}+2^{n-1}$, so the next number is $a_5=18+2^4=34$