gaokao 2022 Q12

gaokao · China · national-B-science 5 marks Sequences and Series Evaluation of a Finite or Infinite Sum
Given that $f(x), g(x)$ have domain $\mathbf{R}$, and $f(x) + g(2-x) = 5, g(x) - f(x-4) = 7$. If the graph of $y = g(x)$ is symmetric about the line $x = 2$, and $g(2) = 4$, then $\sum_{k=1}^{22} f(k) =$
A. $-21$
B. $-22$
C. $-23$
D. $-24$
Given that $f(x), g(x)$ have domain $\mathbf{R}$, and $f(x) + g(2-x) = 5, g(x) - f(x-4) = 7$. If the graph of $y = g(x)$ is symmetric about the line $x = 2$, and $g(2) = 4$, then $\sum_{k=1}^{22} f(k) =$\\
A. $-21$\\
B. $-22$\\
C. $-23$\\
D. $-24$