CEMC Fermat, 2003

Number theory Difficulty 3.0 AMC 10/12 Find the answer Canada

A sequence of numbers has 6 as its first term, and every term after the first is defined as follows: If a term, $t$ , is even, the next term in the sequence is $\frac{1}{2}t$ . If a term, $s$ , is odd, the next term is $3s+1$ . Thus, the first four terms in the sequence are 6, 3, 10, 5. The 100th term is

(A) $1$ (B) $2$ (C) $3$ (D) $4$ (E) $6$

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