| 类别 | 描述 |
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|等差数列 | 等差数列是指数列中每一项与前一项的差值相等，通项公式为<br>an=a1+(n-1)d，其中a1为首项，d为公差，求和公式为Sn=n(a1+an)/2，等差数列具有单调性，如果每项都大于或等于前一项，则为单调不减；反之为单调不增，等差数列还有有界性和极限性质，即数列的所有项都有上界和下界，且当项数趋近于无穷大时，数列会趋近于一个常数值，等差数列在几何中的应用包括计算等比数列的面积、体积等。 |
|等比数列 | 等比数列是指数列中每一项与前一项的比值相等，通项公式为<br>an=a1*q^(n-1)，其中a1为首项，q为公比，求和公式为Sn=a1(1-q^n)/(1-q)，当q不等于1时适用，等比数列也具有单调性和有界性，但与等差数列不同的是，等比数列的项可能会趋近于0或无穷大，取决于公比的取值范围，等比数列在几何中的应用包括计算等比数列的面积、体积等。 |
|斐波那契数列 | 斐波那契数列是一种特殊的递归数列，每一项都是前两项之和，通常表示为F(n)=F(n-1)+F(n-2)，其中F(1)=F(2)=1，斐波那契数列在自然界中有许多应用，如植物的叶序、蜂窝结构等。 |
|其他特殊数列 | 除了上述常见数列外，还有一些特殊数列如算术序列（每项都是常数）、几何序列（每项都是前一项的固定倍数）等，这些数列在特定情况下也有其独特的性质和应用。 |
高中数学中的数列主要包括等差数列、等比数列和斐波那契数列等，每种数列都有其独特的性质和应用，掌握这些数列对于提高数学能力具有重要意义。
