一、选择题
题目1：已知函数\(f(x)=ax^2+bx+c\)，若\(f(1)=2\)，\(f(2)=5\)，\(f(3)=8\)，则\(a+b+c=\)
答案解析：
首先，我们可以根据题目给出的三个点来列出三个方程：
\[
\begin{cases}
a + b + c = 2 \\
4a + 2b + c = 5 \\
9a + 3b + c = 8
\end{cases}
\]
接下来，我们可以通过解这个方程组来找到\(a\)、\(b\)和\(c\)的值。首先，我们可以用第一个方程减去第二个方程，得到：
\[
5a + b = -1
\]
然后，我们用第二个方程减去第三个方程，得到：
\[
5a + b = -3
\]
这样，我们就得到了两个相等的方程，这意味着它们是同一个方程。因此，我们可以得出\(a = 0\)。将\(a = 0\)代入第一个方程，得到\(b + c = 2\)。再将\(a = 0\)代入第二个方程，得到\(b + c = 5\)。这样，我们就可以得出\(b = 3\)，\(c = -1\)。
最后，将\(a\)、\(b\)和\(c\)的值代入原方程，得到：
\[
a + b + c = 0 + 3 - 1 = 2
\]
答案： 2
二、填空题
题目2：若等差数列\(\{a_n\}\)的首项为\(a_1\)，公差为\(d\)，则第\(n\)项\(a_n\)的通项公式为$a_n = ________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________
