## 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

by M7MBA » Tue May 04, 2021 7:12 am

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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