Question 22
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.
For example, consider the sample sequence $23,$ $18,$ $9,$ $81,$ $76,$ $\ldots.$
Find the $98$th term of the sequence that begins $98,$ $49,$ $\ldots.$
**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.
For example, consider the sample sequence $23,$ $18,$ $9,$ $81,$ $76,$ $\ldots.$
Find the $98$th term of the sequence that begins $98,$ $49,$ $\ldots.$