CEMC Cayley, 2008

Combinatorics Difficulty 2.0 Junior Find the answer Canada

The first term of a sequence is $20$ . If a term in the sequence is $t$ and $t$ is even, the next term is $\frac{1}{2}t$ . If a term in the sequence is $t$ and $t$ is odd, the next term is $3t+1$ . Therefore, the first three terms in the sequence are $20, 10, 5$ . What is the $10$ th term of the sequence?

(A) $2$ (B) $4$ (C) $5$ (D) $1$ (E) $8$

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