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March 26th, 2016, 05:24 PM   #1
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How would I find the algebraic formula for this geometric pattern?

Help me find the algebraic equation for the pic I posted! Please!
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 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
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Quote:
 Originally Posted by Country Boy 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?
The number of triangles could follow the equation 2^(x-1). 2^(1-1) = 2^0 = 1, 2^(2-1) = 2^1 = 2, and 2^(3-1) = 2^2 = 4. The perimeter could be 2 greater than the number of triangles. I'm not going to guarantee that's the pattern without having more diagrams to look at.

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
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Quote:
 Originally Posted by skipjack You're not asked for the number of triangles
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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