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You get a sequence of doubled triangular numbers. This sequence can also be represented by Un = n*(n + 1), [products of pairs of consecutive integers]
Triangular numbers are numbers in the sequence 1, 1+2, 1+2+3, 1+2+3+4. This sequence can be represented by triangles as follows: (very crude figure with an even cruder browser!)xxxxxxxxxxxxxxxxxxxxand so on.The nth term of this sequence is n*(n+1)/2.Triangular numbers are numbers in the sequence 1, 1+2, 1+2+3, 1+2+3+4. This sequence can be represented by triangles as follows: (very crude figure with an even cruder browser!)xxxxxxxxxxxxxxxxxxxxand so on.The nth term of this sequence is n*(n+1)/2.
I'm guessing your sequence is 1, 3, 6, 10, 15, ... In which case it continues: 21, 28, 36, 45, 55, 66, ... (These are the triangular numbers.)
The 18th triangular number is calculated using the formula ( T_n = \frac{n(n + 1)}{2} ), where ( n ) is the position in the sequence. For ( n = 18 ), this gives ( T_{18} = \frac{18 \times 19}{2} = 171 ). Therefore, the 18th triangular number is 171.
A triangular dipyramid.A triangular dipyramid.A triangular dipyramid.A triangular dipyramid.