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解答 - 几何数列

公比是：

r = 0.0039001560062402497

r=0.0039001560062402497

该系列的和是：

s = 3861

s=3861

此系列的通用形式是：

a_{n} = 3846 \cdot {0.0039001560062402497}^{n - 1}

a_n=3846*0.0039001560062402497^(n-1)

这个序列的第n项是：

3846, 15, 0.05850234009360375, 0.00022816825309517842, 8.898917827425056 E - 07, 3.4707167813670267 E - 09, 1.3536336900807438 E - 11, 5.2793825666175655 E - 14, 2.0590415626433562 E - 16, 8.030583317641795 E - 19

3846,15,0.05850234009360375,0.00022816825309517842,8.898917827425056E-07,3.4707167813670267E-09,1.3536336900807438E-11,5.2793825666175655E-14,2.0590415626433562E-16,8.030583317641795E-19

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：

$a_{2} a_{1} = \frac{15}{3846} = 0.0039001560062402497$

该序列的公比（ $r$ ）保持不变，并且等于两个连续项的商。
$r = 0.0039001560062402497$

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： $a = 3, 846$ 、公比： $r = 0.0039001560062402497$ 和元素数目 $n = 2$ 插入几何级数求和公式：

$s_{2} = 3846 * ((1 - {0.0039001560062402497}^{2}) / (1 - 0.0039001560062402497))$

$s_{2} = 3846 * ((1 - 1.5211216873011895 E - 05) / (1 - 0.0039001560062402497))$

$s_{2} = 3846 * (0.999984788783127 / (1 - 0.0039001560062402497))$

$s_{2} = 3846 * (0.999984788783127 / 0.9960998439937597)$

$s_{2} = 3846 \cdot 1.0039001560062404$

$s_{2} = 3861.0000000000005$

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： $a = 3, 846$ 和公比： $r = 0.0039001560062402497$ 插入几何级数的公式：

$a_{n} = 3846 \cdot {0.0039001560062402497}^{n - 1}$

4. 找到第n项

使用通用公式找到第n项

$a_{1} = 3846$

$a_{2} = a_{1} \cdot r^{n - 1} = 3846 \cdot {0.0039001560062402497}^{2 - 1} = 3846 \cdot {0.0039001560062402497}^{1} = 3846 \cdot 0.0039001560062402497 = 15$

$a_{3} = a_{1} \cdot r^{n - 1} = 3846 \cdot {0.0039001560062402497}^{3 - 1} = 3846 \cdot {0.0039001560062402497}^{2} = 3846 \cdot 1.5211216873011895 E - 05 = 0.05850234009360375$

$a_{4} = a_{1} \cdot r^{n - 1} = 3846 \cdot {0.0039001560062402497}^{4 - 1} = 3846 \cdot {0.0039001560062402497}^{3} = 3846 \cdot 5.932611884950037 E - 08 = 0.00022816825309517842$

$a_{5} = a_{1} \cdot r^{n - 1} = 3846 \cdot {0.0039001560062402497}^{5 - 1} = 3846 \cdot {0.0039001560062402497}^{4} = 3846 \cdot 2.3138111875780176 E - 10 = 8.898917827425056 E - 07$

$a_{6} = a_{1} \cdot r^{n - 1} = 3846 \cdot {0.0039001560062402497}^{6 - 1} = 3846 \cdot {0.0039001560062402497}^{5} = 3846 \cdot 9.024224600538291 E - 13 = 3.4707167813670267 E - 09$

$a_{7} = a_{1} \cdot r^{n - 1} = 3846 \cdot {0.0039001560062402497}^{7 - 1} = 3846 \cdot {0.0039001560062402497}^{6} = 3846 \cdot 3.5195883777450434 E - 15 = 1.3536336900807438 E - 11$

$a_{8} = a_{1} \cdot r^{n - 1} = 3846 \cdot {0.0039001560062402497}^{8 - 1} = 3846 \cdot {0.0039001560062402497}^{7} = 3846 \cdot 1.3726943750955708 E - 17 = 5.2793825666175655 E - 14$

$a_{9} = a_{1} \cdot r^{n - 1} = 3846 \cdot {0.0039001560062402497}^{9 - 1} = 3846 \cdot {0.0039001560062402497}^{8} = 3846 \cdot 5.3537222117611967 E - 20 = 2.0590415626433562 E - 16$

$a_{10} = a_{1} \cdot r^{n - 1} = 3846 \cdot {0.0039001560062402497}^{10 - 1} = 3846 \cdot {0.0039001560062402497}^{9} = 3846 \cdot 2.0880351839942265 E - 22 = 8.030583317641795 E - 19$

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几何数列