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There is no specific name. In particular, if the first term of the sequence is not 1, then the pattern may not be easily recognised. However, if the first number is 1, the sequence is the triangular numbers.

t(1) = 1

t(2) = t(1) + 2 = 1 + 2 = 3

t(3) = t(2) + 3 = 3 + 3 = 6

t(4) = t(3) + 4 = 6 + 4 = 10 and so on.



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