Concept: The question tests on sequences/series


Notice that if  i = 1 and j = 2, A(1) = 2*A(2)

=>A(2) = A(1)/2

Again if, i = 1 and j = 3, A(1) = 3*A(3) [ i is not necessarily equal to j]

So A(3) = A(1)/3

 => A(1), A(1)/2, A(1)/3, A(1)/4 can represent the series

Clearly A(1) is the ONLY integer and II is true  (Eliminate A and C)

Also, since A(1) is a positive integer, no other numbers following it can be negative. So III is true too.

(Eliminate B)

Now, 2*A(100) = A(99) + A(98)
=>2*A(1)/100 = A(1)/99 + A(1)/98 (cancel A(1) here)
=>2/100 = 1/99 + 1/98
 Not true (Incorrect conceptually)

So eliminate E. (option D)