In the first quadrant of the rectangular coordinate plane; a square $A _ { 1 }$ is drawn with two sides on the coordinate axes and one vertex on the line $\mathrm { d } : \mathrm { y } = 4 - \mathrm { x }$. Then, a square $A _ { 2 }$ adjacent to the square $A _ { 1 }$ with one side on the x-axis and one vertex on line d is drawn. Continuing in a similar manner, a sequence of squares $\mathrm { A } _ { 1 } , \mathrm {~A} _ { 2 } , \mathrm {~A} _ { 3 } , \ldots$ is obtained as shown in the figure. Accordingly, what is the sum of the areas of all the squares $\mathbf { A } _ { \mathbf { n } }$ obtained in square units?
A) $\frac { 9 } { 2 }$
B) $\frac { 11 } { 2 }$
C) $\frac { 14 } { 3 }$
D) $\frac { 16 } { 3 }$
E) $\frac { 20 } { 3 }$

For a geometric sequence $(a_n)$ with all positive terms and common ratio $r$
$$\begin{aligned} & a_1 + \frac{1}{2} + r \\ & a_7^2 = a_5 + 12 \cdot a_3 \end{aligned}$$
the equalities are given.

In a census conducted on January 1, 2015, a city with a population of 810,000 had population counts on January 1 each year from 2016 to 2023. In each of the first four years after 2015, the population increased by a ratio of $\frac{1}{10}$ compared to the previous year, and in each of the following four years, the population increased by a ratio of $\frac{1}{11}$ compared to the previous year.
Accordingly, what was the population of this city in the census conducted on January 1, 2023?
A) $2^{20}$ B) $3^{13}$ C) $5^{9}$ D) $6^{8}$ E) $10^{6}$