数学课前练习

1. 已知函数\(y = \sin(\omega x + \displaystyle \frac{\pi}{6})(\omega > 0)\)在区间\((0,\pi)\)恰有3个零点，则\(\omega\)的取值范围是（）

A. \((\displaystyle \frac{7}{6},\displaystyle \frac{17}{6}]\)

B. \((0,\displaystyle \frac{23}{6}]\)

C. \([\displaystyle \frac{17}{6},\displaystyle \frac{23}{6})\)

D. \((\displaystyle \frac{17}{6},\displaystyle \frac{23}{6}]\)

2. 数列\(\{a_n\}\)中，已知\(S_1 = 1\)，\(S_2 = 2\)，且\(S_{n+1} + 2S_{n-1} = 3S_n(n \geq 2且n \in N^*)\)，则此数列的通项公式为（）

A. \(a_n = 1(n \in N^*)\)

B. \(a_n = 2^{n-1}(n \in N^*)\)

C. \(a_n = \begin{cases}1,n=1 \\ 2^{n-2},n \geq 2,n \in N^*\end{cases}\)

D. \(a_n = \begin{cases}1,n=1 \\ 2^{n-1},n \geq 2,n \in N^*\end{cases}\)