第n项规则

通过找出等差数列的公差和第零项，写出其第n项表达式，并用它来确定数列中的任意一项，或判断某个给定的数是否属于该数列。

Find the nth-term expression for an arithmetic sequence by identifying the common difference and the zero-term, and use it to determine any term in the sequence or test whether a given number belongs to the sequence

学习证据 / Evidence

• 推导出等差数列（如 3, 7, 11, 15, …）的第n项规则为 4n − 1
• 利用第n项公式求出第50项或第100项，而不必列出前面的所有项
• 判断一个给定的数（例如 99）是否是指定等差数列中的某一项

• Derive the nth-term rule for an arithmetic sequence such as 3, 7, 11, 15, … as 4n − 1
• Use an nth-term formula to find the 50th or 100th term without listing all preceding terms
• Determine whether a given number (e.g., 99) is a term in a specified arithmetic sequence

评估问题 / Assessment

如果给{{name}}数列 4, 7, 10, 13…，他们能否找到第n项的公式，并利用它来检验例如100是否在该数列中？

If {{name}} is given the sequence 4, 7, 10, 13…, can they find a formula for the nth term — and use it to check whether, say, 100 is in the sequence?