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Challenge Response 186


Investigating the sequence

Note that the sequence consists of a 1, two 2's, three 3's and so on. If the sequence continues to the last no, we would have 1 + 2 +… + n = n (n + 1) / 2 terms.

We can verify that (44 × 45) / 2 = 990. That is, the 990th term is the last 44, and the next 45 terms will be 45.

Therefore the thousandth term shall be 45.

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