The sequence \(a_1, a_2, a_3, \ldots , a_n, \ldots\) is such that \(i \cdot a_i=j \cdot a_j\) for any pair of positive

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The sequence \(a_1, a_2, a_3, \ldots , a_n, \ldots\) is such that \(i \cdot a_i=j \cdot a_j\) for any pair of positive integers \((i,j).\) If \(a_1\) is a positive integer, which of the following could be true?

I. \(2\cdot a_{100}=a_{99}+a_{98}\)

II. \(a_1\) is the only integer in the sequence.

III. The sequence does not contain negative numbers.

A. I only
B. II only
C. I and III only
D. II and III only
E. I, II, and III

Answer: D

Source: GMAT Club Tests