Consider an arithmetic progression sum \(1+2+3+\cdots \).

1 is the first term, 2 is the second term, etc.

The cumulative sum is obtained by adding all the terms up to a certain point. For example, the cumulative sum of the first 5 terms is \(1 + 2 + 3 + 4 + 5 = 15\).

How many terms out does the cumulative sum first exceed 100?

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