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解答 - 几何数列

公比是：

r = 0.18181818181818182

r=0.18181818181818182

该系列的和是：

s = 156

s=156

此系列的通用形式是：

a_{n} = 132 \cdot {0.18181818181818182}^{n - 1}

a_n=132*0.18181818181818182^(n-1)

这个序列的第n项是：

132, 24, 4.363636363636363, 0.7933884297520661, 0.14425244177310295, 0.026227716686018716, 0.004768675761094313, 0.0008670319565626023, 0.00015764217392047315, 2.8662213440086027 E - 05

132,24,4.363636363636363,0.7933884297520661,0.14425244177310295,0.026227716686018716,0.004768675761094313,0.0008670319565626023,0.00015764217392047315,2.8662213440086027E-05

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：

$a_{2} a_{1} = \frac{24}{132} = 0.18181818181818182$

该序列的公比（ $r$ ）保持不变，并且等于两个连续项的商。
$r = 0.18181818181818182$

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： $a = 132$ 、公比： $r = 0.18181818181818182$ 和元素数目 $n = 2$ 插入几何级数求和公式：

$s_{2} = 132 * ((1 - {0.18181818181818182}^{2}) / (1 - 0.18181818181818182))$

$s_{2} = 132 * ((1 - 0.03305785123966942) / (1 - 0.18181818181818182))$

$s_{2} = 132 * (0.9669421487603306 / (1 - 0.18181818181818182))$

$s_{2} = 132 * (0.9669421487603306 / 0.8181818181818181)$

$s_{2} = 132 \cdot 1.1818181818181819$

$s_{2} = 156$

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： $a = 132$ 和公比： $r = 0.18181818181818182$ 插入几何级数的公式：

$a_{n} = 132 \cdot {0.18181818181818182}^{n - 1}$

4. 找到第n项

使用通用公式找到第n项

$a_{1} = 132$

$a_{2} = a_{1} \cdot r^{n - 1} = 132 \cdot {0.18181818181818182}^{2 - 1} = 132 \cdot {0.18181818181818182}^{1} = 132 \cdot 0.18181818181818182 = 24$

$a_{3} = a_{1} \cdot r^{n - 1} = 132 \cdot {0.18181818181818182}^{3 - 1} = 132 \cdot {0.18181818181818182}^{2} = 132 \cdot 0.03305785123966942 = 4.363636363636363$

$a_{4} = a_{1} \cdot r^{n - 1} = 132 \cdot {0.18181818181818182}^{4 - 1} = 132 \cdot {0.18181818181818182}^{3} = 132 \cdot 0.006010518407212622 = 0.7933884297520661$

$a_{5} = a_{1} \cdot r^{n - 1} = 132 \cdot {0.18181818181818182}^{5 - 1} = 132 \cdot {0.18181818181818182}^{4} = 132 \cdot 0.0010928215285841132 = 0.14425244177310295$

$a_{6} = a_{1} \cdot r^{n - 1} = 132 \cdot {0.18181818181818182}^{6 - 1} = 132 \cdot {0.18181818181818182}^{5} = 132 \cdot 0.00019869482337892967 = 0.026227716686018716$

$a_{7} = a_{1} \cdot r^{n - 1} = 132 \cdot {0.18181818181818182}^{7 - 1} = 132 \cdot {0.18181818181818182}^{6} = 132 \cdot 3.612633152344176 E - 05 = 0.004768675761094313$

$a_{8} = a_{1} \cdot r^{n - 1} = 132 \cdot {0.18181818181818182}^{8 - 1} = 132 \cdot {0.18181818181818182}^{7} = 132 \cdot 6.568423913353048 E - 06 = 0.0008670319565626023$

$a_{9} = a_{1} \cdot r^{n - 1} = 132 \cdot {0.18181818181818182}^{9 - 1} = 132 \cdot {0.18181818181818182}^{8} = 132 \cdot 1.1942588933369177 E - 06 = 0.00015764217392047315$

$a_{10} = a_{1} \cdot r^{n - 1} = 132 \cdot {0.18181818181818182}^{10 - 1} = 132 \cdot {0.18181818181818182}^{9} = 132 \cdot 2.1713798060671234 E - 07 = 2.8662213440086027 E - 05$

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几何数列