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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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Q: What is the name for the rule of adding one more each time in a sequence?
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