The sequence $x _ { n }$ is defined by the rules
$$\begin{aligned}
x _ { 1 } & = 7 \\
x _ { n + 1 } & = \frac { 23 x _ { n } - 53 } { 5 x _ { n } + 1 }
\end{aligned}$$
The first three terms in the sequence are $7,3,1$
What is the value of $x _ { 100 }$ ?
A - 5
B 0
C 1
D 3
E 7