CN-LEAGUE 1997

Squence $(x_n)$ satisfies that $x_{n+1}=x_n-x_{n-1}(n\geq2)$ . If $x_1=a,x_2=b$ , $S_n=x_1+x_2+\cdots+x_n$ . Wich one is correct? $\text{(A)}x_{100}=-a,S_{100}=2b-a$ $\text{(B)}x_{100}=-b,S_{100}=2b-a$ $\text{(C)}x_{100}=-a,S_{100}=b-a$ $\text{(D)}x_{100}=-b,S_{100}=b-a$

In regular tetrahedron $ABCD$ , $E\in AB,F\in CD$ , satisfying: $\frac{|AE|}{|EB|}=\frac{|CF|}{|FD|}=\lambda(\lambda\in R_+)$ . Note that $f(\lambda)=\alpha_{\lambda}+\beta_{\lambda}$ , where $\alpha_{\lambda}=<EF,AC>,\alpha_{\lambda}=<EF,BD>$ . $\text{(A)}$ $f(\lambda)$ increases in $(0,+\infty)$ $\text{(B)}$ $f(\lambda)$ decreases in $(0,+\infty)$ $\text{(C)}$ $f(\lambda)$ increases in $(0,1)$ , decreases in $(1,+\infty)$ $\text{(D)}$ $f(\lambda)$ is a fixed value in $(0,+\infty)$

The first item and common difference of an arithmetic sequence are nonnegative intengers. The number of items is not less than $3$ , and the sum of all items is $97^2$ . Then the number of such sequences is $\text{(A)}2 \text{(B)}3 \text{(C)}4 \text{(D)}5$