A geometric sequence $(b_n)$ with first two terms $b_{1} = \frac{4}{3}$ and $b_{2} = 2$ and an arithmetic sequence $(a_n)$ whose common difference equals the common ratio of this geometric sequence are given.
If $b_{7} = a_{11}$, what is $a_{1}$?
A) $\frac{1}{4}$
B) $\frac{1}{8}$
C) $\frac{3}{8}$
D) $\frac{3}{16}$
E) $\frac{5}{16}$