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解答 - 几何数列

公比是：

r = 0.00980392156862745

r=0.00980392156862745

该系列的和是：

s = 2575

s=2575

此系列的通用形式是：

a_{n} = 2550 \cdot {0.00980392156862745}^{n - 1}

a_n=2550*0.00980392156862745^(n-1)

这个序列的第n项是：

2550, 25, 0.2450980392156863, 0.0024029219530949633, 2.3558058363676112 E - 05, 2.3096135650662853 E - 07, 2.2643270245747895 E - 09, 2.2199284554654798 E - 11, 2.1764004465347843 E - 13, 2.1337259279752784 E - 15

2550,25,0.2450980392156863,0.0024029219530949633,2.3558058363676112E-05,2.3096135650662853E-07,2.2643270245747895E-09,2.2199284554654798E-11,2.1764004465347843E-13,2.1337259279752784E-15

查看步骤

逐步解答

1. 找到公比

通过将序列中的任何项除以前一项来找到公比：

$a_{2} a_{1} = \frac{25}{2550} = 0.00980392156862745$

该序列的公比（ $r$ ）保持不变，并且等于两个连续项的商。
$r = 0.00980392156862745$

2. 求和

5 个额外步骤

$s_{n} = a * ((1 - r^{n}) / (1 - r))$

要找到系列的和，将第一项： $a = 2, 550$ 、公比： $r = 0.00980392156862745$ 和元素数目 $n = 2$ 插入几何级数求和公式：

$s_{2} = 2550 * ((1 - {0.00980392156862745}^{2}) / (1 - 0.00980392156862745))$

$s_{2} = 2550 * ((1 - 9.611687812379854 E - 05) / (1 - 0.00980392156862745))$

$s_{2} = 2550 * (0.9999038831218762 / (1 - 0.00980392156862745))$

$s_{2} = 2550 * (0.9999038831218762 / 0.9901960784313726)$

$s_{2} = 2550 \cdot 1.0098039215686274$

$s_{2} = 2575$

3. 找到通用形式

$a_{n} = a \cdot r^{n - 1}$

要找到系列的通用形式，将第一项： $a = 2, 550$ 和公比： $r = 0.00980392156862745$ 插入几何级数的公式：

$a_{n} = 2550 \cdot {0.00980392156862745}^{n - 1}$

4. 找到第n项

使用通用公式找到第n项

$a_{1} = 2550$

$a_{2} = a_{1} \cdot r^{n - 1} = 2550 \cdot {0.00980392156862745}^{2 - 1} = 2550 \cdot {0.00980392156862745}^{1} = 2550 \cdot 0.00980392156862745 = 25$

$a_{3} = a_{1} \cdot r^{n - 1} = 2550 \cdot {0.00980392156862745}^{3 - 1} = 2550 \cdot {0.00980392156862745}^{2} = 2550 \cdot 9.611687812379854 E - 05 = 0.2450980392156863$

$a_{4} = a_{1} \cdot r^{n - 1} = 2550 \cdot {0.00980392156862745}^{4 - 1} = 2550 \cdot {0.00980392156862745}^{3} = 2550 \cdot 9.423223345470445 E - 07 = 0.0024029219530949633$

$a_{5} = a_{1} \cdot r^{n - 1} = 2550 \cdot {0.00980392156862745}^{5 - 1} = 2550 \cdot {0.00980392156862745}^{4} = 2550 \cdot 9.238454260265142 E - 09 = 2.3558058363676112 E - 05$

$a_{6} = a_{1} \cdot r^{n - 1} = 2550 \cdot {0.00980392156862745}^{6 - 1} = 2550 \cdot {0.00980392156862745}^{5} = 2550 \cdot 9.057308098299158 E - 11 = 2.3096135650662853 E - 07$

$a_{7} = a_{1} \cdot r^{n - 1} = 2550 \cdot {0.00980392156862745}^{7 - 1} = 2550 \cdot {0.00980392156862745}^{6} = 2550 \cdot 8.879713821861919 E - 13 = 2.2643270245747895 E - 09$

$a_{8} = a_{1} \cdot r^{n - 1} = 2550 \cdot {0.00980392156862745}^{8 - 1} = 2550 \cdot {0.00980392156862745}^{7} = 2550 \cdot 8.705601786139136 E - 15 = 2.2199284554654798 E - 11$

$a_{9} = a_{1} \cdot r^{n - 1} = 2550 \cdot {0.00980392156862745}^{9 - 1} = 2550 \cdot {0.00980392156862745}^{8} = 2550 \cdot 8.534903711901114 E - 17 = 2.1764004465347843 E - 13$

$a_{10} = a_{1} \cdot r^{n - 1} = 2550 \cdot {0.00980392156862745}^{10 - 1} = 2550 \cdot {0.00980392156862745}^{9} = 2550 \cdot 8.367552658726583 E - 19 = 2.1337259279752784 E - 15$

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几何数列