Gaokao Math Practice Question
12. (5 分) 设 $\triangle A_{n} B_{n} C_{n}$ 的三边长分别为 $a_{n}, b_{n}, c_{n}, \triangle A_{n} B_{n} C_{n}$ 的面积为 $S_{n}, n=1$ , 2, 3... 若 $b_{1}>c_{1}, b_{1}+c_{1}=2 a_{1}, a_{n+1}=a_{n}, b_{n+1}=\frac{c_{n}+a_{n}}{2}, c_{n+1}=\frac{b_{n}+a_{n}}{2}$, 则 ( )
- A.$\left\{S_{n}\right\}$ 为递减数列
- B.$\left\{S_{n}\right\}$ 为递增数列
- C.$\left\{S_{2 n-1}\right\}$ 为递增数列, $\left\{S_{2 n}\right\}$ 为递减数列
- D.$\left\{S_{2 n-1}\right\}$ 为递减数列, $\left\{S_{2 n}\right\}$ 为递增数列
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