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解答 - 几何数列

公比是：

r = 8.846153846153847

r=8.846153846153847

该系列的和是：

s = 640

s=640

此系列的通用形式是：

a_{n} = 65 \cdot {8.846153846153847}^{n - 1}

a_n=65*8.846153846153847^(n-1)

这个序列的第n项是：

65, 575, 5086.538461538462, 44996.301775147935, 398044.2080109241, 3521160.3016350977, 31148725.745233558, 275546420.05398923, 2437526023.55452, 21562730208.36691

65,575,5086.538461538462,44996.301775147935,398044.2080109241,3521160.3016350977,31148725.745233558,275546420.05398923,2437526023.55452,21562730208.36691

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：

$a_{2} a_{1} = \frac{575}{65} = 8.846153846153847$

该序列的公比（ $r$ ）保持不变，并且等于两个连续项的商。
$r = 8.846153846153847$

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： $a = 65$ 、公比： $r = 8.846153846153847$ 和元素数目 $n = 2$ 插入几何级数求和公式：

$s_{2} = 65 * ((1 - {8.846153846153847}^{2}) / (1 - 8.846153846153847))$

$s_{2} = 65 * ((1 - 78.2544378698225) / (1 - 8.846153846153847))$

$s_{2} = 65 * (- 77.2544378698225 / (1 - 8.846153846153847))$

$s_{2} = 65 * (- 77.2544378698225 / - 7.846153846153847)$

$s_{2} = 65 \cdot 9.846153846153847$

$s_{2} = 640$

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： $a = 65$ 和公比： $r = 8.846153846153847$ 插入几何级数的公式：

$a_{n} = 65 \cdot {8.846153846153847}^{n - 1}$

4. 找到第n项

使用通用公式找到第n项

$a_{1} = 65$

$a_{2} = a_{1} \cdot r^{n - 1} = 65 \cdot {8.846153846153847}^{2 - 1} = 65 \cdot {8.846153846153847}^{1} = 65 \cdot 8.846153846153847 = 575$

$a_{3} = a_{1} \cdot r^{n - 1} = 65 \cdot {8.846153846153847}^{3 - 1} = 65 \cdot {8.846153846153847}^{2} = 65 \cdot 78.2544378698225 = 5086.538461538462$

$a_{4} = a_{1} \cdot r^{n - 1} = 65 \cdot {8.846153846153847}^{4 - 1} = 65 \cdot {8.846153846153847}^{3} = 65 \cdot 692.2507965407375 = 44996.301775147935$

$a_{5} = a_{1} \cdot r^{n - 1} = 65 \cdot {8.846153846153847}^{5 - 1} = 65 \cdot {8.846153846153847}^{4} = 65 \cdot 6123.757046321909 = 398044.2080109241$

$a_{6} = a_{1} \cdot r^{n - 1} = 65 \cdot {8.846153846153847}^{6 - 1} = 65 \cdot {8.846153846153847}^{5} = 65 \cdot 54171.696948232275 = 3521160.3016350977$

$a_{7} = a_{1} \cdot r^{n - 1} = 65 \cdot {8.846153846153847}^{7 - 1} = 65 \cdot {8.846153846153847}^{6} = 65 \cdot 479211.1653112855 = 31148725.745233558$

$a_{8} = a_{1} \cdot r^{n - 1} = 65 \cdot {8.846153846153847}^{8 - 1} = 65 \cdot {8.846153846153847}^{7} = 65 \cdot 4239175.693138296 = 275546420.05398923$

$a_{9} = a_{1} \cdot r^{n - 1} = 65 \cdot {8.846153846153847}^{9 - 1} = 65 \cdot {8.846153846153847}^{8} = 65 \cdot 37500400.362377234 = 2437526023.55452$

$a_{10} = a_{1} \cdot r^{n - 1} = 65 \cdot {8.846153846153847}^{10 - 1} = 65 \cdot {8.846153846153847}^{9} = 65 \cdot 331734310.89795244 = 21562730208.36691$

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