1. Given a non-constant sequence $\left\{a_{i}\right\}$ satisfies $a_{i+1}^{2}-a_{i} a_{i+1}+a_{i}^{2}=0$, and $a_{i+1} \neq a_{i-1}, i=1,2, \cdots, n$. For a given natural number $n, a_{1}=a_{n+1}=1$, then $\sum_{i=0}^{n-1} a_{i}$ equals
A. 2
B. -1
C. 1
D. 0
1. D Because the sequence $\left\{a_{n}\right\}$ is a non-constant sequence and $a_{i+1} \neq a_{i-1}, i=1,2, \cdots, n$, so, $a_{i+1}+a_{i-1}=a_{i}, i=1$, $2, \cdots, n$. Therefore, we get $a_{0}=a_{1}-a_{2}, a_{1}=a_{2}-a_{3}, \cdots, a_{n-2}=a_{n-1}-a_{n}, a_{n-1}=a_{n}-a_{n+1}$.
Thus, $\sum_{i=0}^{n-1} a_{i}=a_{1}-a_{n+1}=0$. Hence, the answer is D.