February 11th, 2019, 02:40 PM  #1 
Newbie Joined: Feb 2019 From: Australia Posts: 1 Thanks: 0  Help!!
Ok, so I've been working on this question for days and nothing has been working. The requirements are a rule (algebraic formula) for the matchstick pattern (e.g. x= n(n1) 4n etc.) Here is the table  PM me for the visual representation. Item (x)= 1, 2, 3, 4, Matchsticks (n)= 4, 12, 24, 40, any help would be much appreciated. (Just to clarify, 1 item = 4 matchsticks.) Last edited by skipjack; February 12th, 2019 at 05:04 PM. 
February 11th, 2019, 03:46 PM  #2 
Math Team Joined: Jul 2011 From: Texas Posts: 3,016 Thanks: 1600 
1 ... 2x2 2 ... 3X4 3 ... 4x6 4 ... 5x8 see a pattern? 
February 11th, 2019, 11:59 PM  #3 
Global Moderator Joined: Dec 2006 Posts: 20,965 Thanks: 2214 
Hint: evaluate $\displaystyle \frac{\sqrt{2n + 1}}{2}$ for $n\,=$ 4, 12, 24, 40, etc.

February 12th, 2019, 04:49 AM  #4 
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 14,597 Thanks: 1038 
Compare to triangulars: 1,3,6,10, ..... 4,12,24,40, ..... 
February 12th, 2019, 05:12 AM  #5 
Senior Member Joined: Dec 2015 From: somewhere Posts: 632 Thanks: 91 
The sequence (n)= 4,12,24,40... etc , is 2n(n+1) .

February 12th, 2019, 06:17 AM  #6 
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 14,597 Thanks: 1038  
February 12th, 2019, 08:11 AM  #7 
Global Moderator Joined: Dec 2006 Posts: 20,965 Thanks: 2214 
Except when it's four times.
