Page 1 of 1
A sequence challenge
Posted: Mon Mar 28, 2011 11:23 am
by James Hall
The head of maths here has presented me with a sequence. It was apparently in an old year 7 question sheet, and it has flummoxed the entire maths department. What are the next few terms and/or what is the formula for the sequence?
Here it is:
1, 2, 6, 15, 16, 16, —15, —17
Any thoughts welcome!
Re: A sequence challenge
Posted: Mon Mar 28, 2011 7:22 pm
by JackHurst
I absolutely despise these sort of questions, there are infinitely many formulas that will generate that sequence of numbers, so how are you meant to know which one is the one the question setter was thinking of?
Re: A sequence challenge
Posted: Mon Mar 28, 2011 8:10 pm
by Charlie Reams
JackHurst wrote:I absolutely despise these sort of questions, there are infinitely many formulas that will generate that sequence of numbers, so how are you meant to know which one is the one the question setter was thinking of?
Parsimony!
But yes, I agree.
Re: A sequence challenge
Posted: Mon Mar 28, 2011 8:42 pm
by Hugh Binnie
Re: A sequence challenge
Posted: Mon Mar 28, 2011 11:18 pm
by JackHurst
Bearing in mind my previous gripe, what comes next after 1, 2, 4, 8, 16?
Offer an explanation when you post your answer.
Re: A sequence challenge
Posted: Tue Mar 29, 2011 5:53 am
by Joseph Krol
17 because it goes +1+2+4+8 and then repeats.
Re: A sequence challenge
Posted: Tue Mar 29, 2011 10:24 am
by Gavin Chipper
I remember at school we did this thing drawing lines through a circle or something and it was 31.
Re: A sequence challenge
Posted: Tue Mar 29, 2011 1:55 pm
by JackHurst
Gavin Chipper wrote:I remember at school we did this thing drawing lines through a circle or something and it was 31.
Yeah, thats what I was thinking of.
http://www.uz.ac.zw/science/maths/zimaths/seq3132.htm
Re: A sequence challenge
Posted: Fri Apr 01, 2011 9:25 pm
by Neil Zussman
James Hall wrote:The head of maths here has presented me with a sequence. It was apparently in an old year 7 question sheet, and it has flummoxed the entire maths department. What are the next few terms and/or what is the formula for the sequence?
Here it is:
1, 2, 6, 15, 16, 16, —15, —17
Any thoughts welcome!
Nth term is:
x+
(x-1)(x-2)(3/2)+
(x-1)(x-2)(x-3)(1/3)+
(x-1)(x-2)(x-3)(x-4)(-5/8)+
(x-1)(x-2)(x-3)(x-4)(x-5)(A)+
(x-1)(x-2)(x-3)(x-4)(x-5)(x-6)(B)+
(x-1)(x-2)(x-3)(x-4)(x-5)(x-6)(x-7)(C)+
(x-1)(x-2)(x-3)(x-4)(x-5)(x-6)(x-7)(x-8)(D)+
(x-1)(x-2)(x-3)(x-4)(x-5)(x-6)(x-7)(x-8)(x-9)(E)+...
Where A,B,C,D are numbers that can easily be worked out, one at a time following the pattern- in each step one more unknown enters the equations (the rest are all multiplied by 0), so it's simple, but time consuming to calculate them. And I reckon a year 7 could do that easily, provided they knew the right technique. It's very repetitive though, I imagine there's an easier way to generate such a sequence.
To answer the question, I think you can literally make the next number in the sequence whatever you like by changing E.
Re: A sequence challenge
Posted: Sat Apr 02, 2011 10:30 am
by Jon O'Neill
Wat
Re: A sequence challenge
Posted: Sat Apr 02, 2011 11:02 pm
by Hugh Binnie
Or 30, if it's factors of (n+1)!.
Re: A sequence challenge
Posted: Sun Apr 03, 2011 2:40 pm
by Gavin Chipper
Jon O'Neill wrote:Wat
I agree.
Re: A sequence challenge
Posted: Thu Apr 07, 2011 5:36 am
by John Gillies
Would someone please solve this. I haven't a f****ing clue and it's driving me nuts!