A formula

[aommaster]

You know these questions when they ask you to find out how many triangle are there in the diagram? Well, is there an actual formula that can be used???

[wolfson]

#ABC = (xS^t+yS^p+rS-(S mod 2)) / f

 

The letters relate to colums if you send me the picture or attach the picture of the traingle(s), then ill be happy to transpose the equation for you..

[aommaster]

umm... i don't really have a picture, i was just generalising, i just wanted to know if there was a formula. Can u explain to me exactly how to find the formula so that i could work it out by myself

[wolfson]

Could someone please help me find a picture of a triangle's with a triangle, a sequence of top line 1 triangle next two and so on.... This would be much appreciated

[aommaster]

I found one but of a differnt sequence

[wolfson]

Ok this sequence starts with one triangle (a), and ends with 7 on the end (n):

 

So applying Sn. For Arithmetic Progressions:

 

x(a+n)/2

 

A = first term 1, n = last sum (7), x =number of sequence lines (4)

 

Sn. = 4(1+7)/2 = 16 (remember only the internal sequence triangles).

 

Theorise: calculating 27 lines:

 

1, 3, 5, 7 (triangles going up at rate of 2 added to previous).

 

Sp. = z -1 x d + 1

Z = Line number to find, m = constant sequence difference (2):

 

27 – 1 x d + 1 = 53

 

So the 27-sequence line would contain 53 triangles (internal).

 

So then apply Sn.

 

x(a+n)/2

 

A = first term 1, n = last sum (53), x =number of sequence lines (27)

 

27(1+53)/2 = 729.

 

The total amount of internal triangle in 27 lines would be 729.

 

I hope this helps.

[wolfson]

Oh yes and please feel free to comment or ask questions

[aommaster]

I think youve made a mistake. You only found the number of small triangle, i need you to find EACH AND EVERY triangle. There are bigger trinagle like the whole of the first and second row. lol