6 Let $a_{1}, a_{2}, \cdots$ and $b_{1}, b_{2}, \cdots$ be arithmetic sequences, where $a_{1}=25, b_{1}=75, a_{100}+b_{100}=$ 100 , then the sum of the first 100 terms of the sequence $\left\{a_{n}+b_{n}\right\}$, $S_{100}$, is
A. 2500
B. 7500
C. 10000
D. 200200
6 C. Let $\left\{a_{n}\right\}$ have a common difference of $d_{1}$, and $\left\{b_{n}\right\}$ have a common difference of $d_{2}$. Then the sequence $\left\{a_{n}+b_{n}\right\}$ is an arithmetic sequence with a common difference of $d_{1}+d_{2}$. From $a_{1}+b_{1}=a_{100}+b_{100}$, we know $d_{1}+d_{2}=0$, so $S_{100}=100 \times 100=10000$.