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Algebra Level 4

Suppose that \(s_1,s_2,s_3,\ldots \) is a strictly increasing sequence of positive integers such that the subsequences\( \large s_{s_1}, s_{s_2}, s_{s_3}, \ldots \) and \(\large s_{s_1+1}, s_{s_2+1}, s_{s_3+1}, \ldots \) are both arithmetic progressions.

Then \(s_1,s_2,s_3,\ldots \) follows a/an:

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