Fermat 2023 Part B - Question 15, CEMC UWaterloo

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Difficulty: 5

This problem is tagged with fermat, fermat23, highschool.

(Fermat 2023, Part B, Question 15, CEMC - UWaterloo)

A sequence has $101$ terms, each of which is a positive integer. If a term, $n$, is even, the next term is equal to $\frac{1}{2} n + 1$. If a term, $n$, is odd, the next term is equal to $\frac{1}{2}(n + 1)$. For example, if the first term is $7$, then the second term is $4$ and the third term is $3$. If the first term is $16$, the $101st$ term is
$(A)$ $1$
$(B)$ $2$
$(C)$ $3$
$(D)$ $4$
$(E)$ $5$

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