3. The sequence is recursively defined as $a_{1}=m$ (any positive number), $a_{n+1}=\frac{-1}{a_{n}+1}, n=1,2,3, \cdots$, for which of the following values of $n$ must $a_{n}=m$? The correct choice is ( ).
A. 14
B. 15
C. 16
D. 17
3. C.

Since $a_{1}=m, a_{n+1}=\frac{-1}{a_{n}+1}$, then $a_{2}=\frac{-1}{m+1}, a_{3}=-\frac{m+1}{m}, a_{4}=m, a_{5}=-\frac{1}{m+1}, \cdots$.
Therefore, the sequence is a periodic sequence with a period of 3, and we have $a_{3 k+1}=a_{1}=m(k=0,1,2, \cdots)$. Thus, $a_{16}=a_{1}=m$.