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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:

None of these choices Geometric progression Harmonic progression Arithmetic progression

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Kushal Dey
Mar 25, 2020

Suppose that S(i) is some function of i. Then we have S(Si) an AP, which is a linear function of i. Therefore, S(S(i))=mi+c. This is only possible when S(i) is also a linear function of i which implies S(i) is also an AP.

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