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A formula


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


So applying Sn. For Arithmetic Progressions:




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.




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.

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