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March 26th, 2016, 05:24 PM  #1 
Newbie Joined: Mar 2016 From: Canada Posts: 1 Thanks: 0  How would I find the algebraic formula for this geometric pattern?
Help me find the algebraic equation for the pic I posted! Please! 
March 26th, 2016, 05:26 PM  #2 
Senior Member Joined: Feb 2016 From: Australia Posts: 1,834 Thanks: 649 Math Focus: Yet to find out. 
Have you had a go yourself? Can you see the recurring pattern in each new figure? 
March 26th, 2016, 05:50 PM  #3 
Math Team Joined: Jan 2015 From: Alabama Posts: 3,264 Thanks: 902 
In the first picture there is one triangle, in the second, two, and in the third, four. How many triangles would you guess for the fourth picture? In the first picture, the perimeter is 3, in the second 4, and in the third, 6. What do you think the pattern is?
Last edited by skipjack; March 26th, 2016 at 08:28 PM. 
March 27th, 2016, 02:10 PM  #4  
Senior Member Joined: Oct 2013 From: New York, USA Posts: 660 Thanks: 87  Quote:
Edit: One of the problems asks for what diagram will have a perimeter of 39. My rules would have all the perimeters being 2 greater than a power of 2, which 39 is not, so I can't be right about both parts. Last edited by EvanJ; March 27th, 2016 at 02:13 PM.  
March 27th, 2016, 03:12 PM  #5 
Global Moderator Joined: Dec 2006 Posts: 20,921 Thanks: 2203 
Various patterns are possible. Perhaps the successive perimeters are all greater by 3 than the successive triangular numbers: 0, 1, 3, 6, 10, . . . , 28, 36, . . . which happen to include 36, and as 3 + 36 = 39, the perimeter value of 39 occurs (eventually). You're not asked for the number of triangles, but it's two less than the perimeter for any simple chain of triangles.

March 31st, 2016, 11:32 AM  #6 
Senior Member Joined: Oct 2013 From: New York, USA Posts: 660 Thanks: 87  You're not asked for the number of triangles in general, but you're asked to draw the fourth figure, so you need to know how many triangles it has. This is the type of problem where the pattern may seem obvious to whoever wrote the problem, but it isn't really obvious. 

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