# New year gift 1

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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