Terri produces a sequence of positive integers by following three rules. She starts with a positive integer, then applies the appropriate rule to the result, and continues in this fashion.  
Rule $1$: If the integer is less than $10$, multiply it by $9$.  
Rule $2$: If the integer is even and greater than 9, divide it by $2$.   
Rule $3$: If the integer is odd and greater than $9$, subtract $5$ from it.   
$A$ sample sequence: $23, 18, 9, 81, 76, \cdots$.   
Find the value of the $98^\text{th}$ term of the sequence that begins $98, 49, \cdots$.

Let's think step by step and output the final answer within \boxed{}.
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