已知数列 $\left\{a_n\right\}$ 满足 $a_1=1, a_{n+1}=a_n-\frac{1}{3} a_n^2\left(n \in \mathbf{N}^*\right)$, 则
$\text{A.}$ $2 < 100 a_{100} < \frac{5}{2}$
$\text{B.}$ $\frac{5}{2} < 100 a_{100} < 3$
$\text{C.}$ $3 < 100 a_{100} < \frac{7}{2}$
$\text{D.}$ $\frac{7}{2} < 100 a_{100} < 4$