Question

等差数列 $13$ 、 $16$ 、 $19$ 、 $\dotsc$ 、 $70$ 、 $73$ 中有多少项？

How many terms are in the arithmetic sequence $13,$ $16,$ $19,$ $\dotsc,$ $70,$ $73?$

$20$

$21$

$24$

$60$

$61$

答案：B

知识点：等差数列

难度评级：870

解答：

回忆等差数列的第 $n$ 项为 $a + d(n - 1)$ ，其中 $a$ 是首项， $d$ 是公差。

这里 $a = 13$ ， $d = 3$ 。代入可得所以正确答案是 B。 $\begin{aligned} 73 &= 13 + 3(n - 1) \\ 20&= n - 1 \\ n &= 21. \end{aligned}$

Recall that the $n$ th term of an arithmetic sequence is $a + d(n - 1),$ where $a$ is the first term and $d$ is the common difference.

For us, $a = 13$ and $d = 3.$ Plugging these in, we get that $\begin{aligned} 73 &= 13 + 3(n - 1) \\ 20&= n - 1 \\ n &= 21. \end{aligned}$ Thus, B is the correct answer.

2015 AMC 10A 第 7 题

答案：B

难度评级：870

解答：

其他年份的第 7 题