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解答 - 几何数列

公比是：

r = 0.01084010840108401

r=0.01084010840108401

该系列的和是：

s = 373

s=373

此系列的通用形式是：

a_{n} = 369 \cdot {0.01084010840108401}^{n - 1}

a_n=369*0.01084010840108401^(n-1)

这个序列的第n项是：

369, 4, 0.04336043360433604, 0.0004700318005890086, 5.095195670341557 E - 06, 5.523247339123639 E - 08, 5.987259988209907 E - 10, 6.490254729766837 E - 12, 7.035506482132071 E - 14, 7.626565292284088 E - 16

369,4,0.04336043360433604,0.0004700318005890086,5.095195670341557E-06,5.523247339123639E-08,5.987259988209907E-10,6.490254729766837E-12,7.035506482132071E-14,7.626565292284088E-16

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：

$a_{2} a_{1} = \frac{4}{369} = 0.01084010840108401$

该序列的公比（ $r$ ）保持不变，并且等于两个连续项的商。
$r = 0.01084010840108401$

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： $a = 369$ 、公比： $r = 0.01084010840108401$ 和元素数目 $n = 2$ 插入几何级数求和公式：

$s_{2} = 369 * ((1 - {0.01084010840108401}^{2}) / (1 - 0.01084010840108401))$

$s_{2} = 369 * ((1 - 0.00011750795014725215) / (1 - 0.01084010840108401))$

$s_{2} = 369 * (0.9998824920498528 / (1 - 0.01084010840108401))$

$s_{2} = 369 * (0.9998824920498528 / 0.989159891598916)$

$s_{2} = 369 \cdot 1.010840108401084$

$s_{2} = 373$

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： $a = 369$ 和公比： $r = 0.01084010840108401$ 插入几何级数的公式：

$a_{n} = 369 \cdot {0.01084010840108401}^{n - 1}$

4. 找到第n项

使用通用公式找到第n项

$a_{1} = 369$

$a_{2} = a_{1} \cdot r^{n - 1} = 369 \cdot {0.01084010840108401}^{2 - 1} = 369 \cdot {0.01084010840108401}^{1} = 369 \cdot 0.01084010840108401 = 4$

$a_{3} = a_{1} \cdot r^{n - 1} = 369 \cdot {0.01084010840108401}^{3 - 1} = 369 \cdot {0.01084010840108401}^{2} = 369 \cdot 0.00011750795014725215 = 0.04336043360433604$

$a_{4} = a_{1} \cdot r^{n - 1} = 369 \cdot {0.01084010840108401}^{4 - 1} = 369 \cdot {0.01084010840108401}^{3} = 369 \cdot 1.273798917585389 E - 06 = 0.0004700318005890086$

$a_{5} = a_{1} \cdot r^{n - 1} = 369 \cdot {0.01084010840108401}^{5 - 1} = 369 \cdot {0.01084010840108401}^{4} = 369 \cdot 1.3808118347809097 E - 08 = 5.095195670341557 E - 06$

$a_{6} = a_{1} \cdot r^{n - 1} = 369 \cdot {0.01084010840108401}^{6 - 1} = 369 \cdot {0.01084010840108401}^{5} = 369 \cdot 1.4968149970524766 E - 10 = 5.523247339123639 E - 08$

$a_{7} = a_{1} \cdot r^{n - 1} = 369 \cdot {0.01084010840108401}^{7 - 1} = 369 \cdot {0.01084010840108401}^{6} = 369 \cdot 1.622563682441709 E - 12 = 5.987259988209907 E - 10$

$a_{8} = a_{1} \cdot r^{n - 1} = 369 \cdot {0.01084010840108401}^{8 - 1} = 369 \cdot {0.01084010840108401}^{7} = 369 \cdot 1.758876620533018 E - 14 = 6.490254729766837 E - 12$

$a_{9} = a_{1} \cdot r^{n - 1} = 369 \cdot {0.01084010840108401}^{9 - 1} = 369 \cdot {0.01084010840108401}^{8} = 369 \cdot 1.906641323071022 E - 16 = 7.035506482132071 E - 14$

$a_{10} = a_{1} \cdot r^{n - 1} = 369 \cdot {0.01084010840108401}^{10 - 1} = 369 \cdot {0.01084010840108401}^{9} = 369 \cdot 2.066819862407612 E - 18 = 7.626565292284088 E - 16$

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几何数列