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解答 - 几何数列

公比是：

r = 5.526315789473684

r=5.526315789473684

该系列的和是：

s = 124

s=124

此系列的通用形式是：

a_{n} = 19 \cdot {5.526315789473684}^{n - 1}

a_n=19*5.526315789473684^(n-1)

这个序列的第n项是：

19, 105, 580.2631578947368, 3206.717451523545, 17721.33328473538, 97933.68394195869, 541212.4638897717, 2990910.9846540014, 16528718.59940369, 91342918.57565197

19,105,580.2631578947368,3206.717451523545,17721.33328473538,97933.68394195869,541212.4638897717,2990910.9846540014,16528718.59940369,91342918.57565197

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：

$a_{2} a_{1} = \frac{105}{19} = 5.526315789473684$

该序列的公比（ $r$ ）保持不变，并且等于两个连续项的商。
$r = 5.526315789473684$

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： $a = 19$ 、公比： $r = 5.526315789473684$ 和元素数目 $n = 2$ 插入几何级数求和公式：

$s_{2} = 19 * ((1 - {5.526315789473684}^{2}) / (1 - 5.526315789473684))$

$s_{2} = 19 * ((1 - 30.540166204986146) / (1 - 5.526315789473684))$

$s_{2} = 19 * (- 29.540166204986146 / (1 - 5.526315789473684))$

$s_{2} = 19 * (- 29.540166204986146 / - 4.526315789473684)$

$s_{2} = 19 \cdot 6.526315789473684$

$s_{2} = 124$

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： $a = 19$ 和公比： $r = 5.526315789473684$ 插入几何级数的公式：

$a_{n} = 19 \cdot {5.526315789473684}^{n - 1}$

4. 找到第n项

使用通用公式找到第n项

$a_{1} = 19$

$a_{2} = a_{1} \cdot r^{n - 1} = 19 \cdot {5.526315789473684}^{2 - 1} = 19 \cdot {5.526315789473684}^{1} = 19 \cdot 5.526315789473684 = 105$

$a_{3} = a_{1} \cdot r^{n - 1} = 19 \cdot {5.526315789473684}^{3 - 1} = 19 \cdot {5.526315789473684}^{2} = 19 \cdot 30.540166204986146 = 580.2631578947368$

$a_{4} = a_{1} \cdot r^{n - 1} = 19 \cdot {5.526315789473684}^{4 - 1} = 19 \cdot {5.526315789473684}^{3} = 19 \cdot 168.77460271176554 = 3206.717451523545$

$a_{5} = a_{1} \cdot r^{n - 1} = 19 \cdot {5.526315789473684}^{5 - 1} = 19 \cdot {5.526315789473684}^{4} = 19 \cdot 932.701751828178 = 17721.33328473538$

$a_{6} = a_{1} \cdot r^{n - 1} = 19 \cdot {5.526315789473684}^{6 - 1} = 19 \cdot {5.526315789473684}^{5} = 19 \cdot 5154.4044179978255 = 97933.68394195869$

$a_{7} = a_{1} \cdot r^{n - 1} = 19 \cdot {5.526315789473684}^{7 - 1} = 19 \cdot {5.526315789473684}^{6} = 19 \cdot 28484.8665205143 = 541212.4638897717$

$a_{8} = a_{1} \cdot r^{n - 1} = 19 \cdot {5.526315789473684}^{8 - 1} = 19 \cdot {5.526315789473684}^{7} = 19 \cdot 157416.3676133685 = 2990910.9846540014$

$a_{9} = a_{1} \cdot r^{n - 1} = 19 \cdot {5.526315789473684}^{9 - 1} = 19 \cdot {5.526315789473684}^{8} = 19 \cdot 869932.5578633521 = 16528718.59940369$

$a_{10} = a_{1} \cdot r^{n - 1} = 19 \cdot {5.526315789473684}^{10 - 1} = 19 \cdot {5.526315789473684}^{9} = 19 \cdot 4807522.030297472 = 91342918.57565197$

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