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赵鑫 2022-09-07 21:40:33 +08:00
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$$ a_n = a + (n-1)d \tag{等差数列通项公式} $$
换句话说,任意一个等差数列 $\{a_{n}\}$ 都可以写成:$\{\,a,\,a+d,\,a+2d,\,\cdots,\,a+(n-1)d\,\}$
由等差数列通项公式可以得到以下公式:
$$ n = \dfrac{a_n - a}{d} + 1 \tag{已知首项尾项及公差求项数}$$
等差数列求和公式:
换句话说,任意一个等差数列 $\{a_{n}\}$ 都可以写成:$\{\,a,\,a+d,\,a+2d,\,\cdots,\,a+(n-1)d\,\}$
$$ \dfrac {(a + a_n) \times n}{2} $$
$$ 等差数列各项的和 = \dfrac {(a + a_n) \times n}{2} $$