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解答 - 几何数列

公比是：

r = 0.13157894736842105

r=0.13157894736842105

该系列的和是：

s = 43

s=43

此系列的通用形式是：

a_{n} = 38 \cdot {0.13157894736842105}^{n - 1}

a_n=38*0.13157894736842105^(n-1)

这个序列的第n项是：

38, 5, 0.6578947368421052, 0.08656509695290858, 0.011390144335909022, 0.0014987032020932923, 0.0001971977897491174, 2.5947077598568078 E - 05, 3.414089157706326 E - 06, 4.4922225759293755 E - 07

38,5,0.6578947368421052,0.08656509695290858,0.011390144335909022,0.0014987032020932923,0.0001971977897491174,2.5947077598568078E-05,3.414089157706326E-06,4.4922225759293755E-07

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：

$a_{2} a_{1} = \frac{5}{38} = 0.13157894736842105$

该序列的公比（ $r$ ）保持不变，并且等于两个连续项的商。
$r = 0.13157894736842105$

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： $a = 38$ 、公比： $r = 0.13157894736842105$ 和元素数目 $n = 2$ 插入几何级数求和公式：

$s_{2} = 38 * ((1 - {0.13157894736842105}^{2}) / (1 - 0.13157894736842105))$

$s_{2} = 38 * ((1 - 0.017313019390581715) / (1 - 0.13157894736842105))$

$s_{2} = 38 * (0.9826869806094183 / (1 - 0.13157894736842105))$

$s_{2} = 38 * (0.9826869806094183 / 0.868421052631579)$

$s_{2} = 38 \cdot 1.131578947368421$

$s_{2} = 43$

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： $a = 38$ 和公比： $r = 0.13157894736842105$ 插入几何级数的公式：

$a_{n} = 38 \cdot {0.13157894736842105}^{n - 1}$

4. 找到第n项

使用通用公式找到第n项

$a_{1} = 38$

$a_{2} = a_{1} \cdot r^{n - 1} = 38 \cdot {0.13157894736842105}^{2 - 1} = 38 \cdot {0.13157894736842105}^{1} = 38 \cdot 0.13157894736842105 = 5$

$a_{3} = a_{1} \cdot r^{n - 1} = 38 \cdot {0.13157894736842105}^{3 - 1} = 38 \cdot {0.13157894736842105}^{2} = 38 \cdot 0.017313019390581715 = 0.6578947368421052$

$a_{4} = a_{1} \cdot r^{n - 1} = 38 \cdot {0.13157894736842105}^{4 - 1} = 38 \cdot {0.13157894736842105}^{3} = 38 \cdot 0.0022780288671818047 = 0.08656509695290858$

$a_{5} = a_{1} \cdot r^{n - 1} = 38 \cdot {0.13157894736842105}^{5 - 1} = 38 \cdot {0.13157894736842105}^{4} = 38 \cdot 0.0002997406404186585 = 0.011390144335909022$

$a_{6} = a_{1} \cdot r^{n - 1} = 38 \cdot {0.13157894736842105}^{6 - 1} = 38 \cdot {0.13157894736842105}^{5} = 38 \cdot 3.943955794982348 E - 05 = 0.0014987032020932923$

$a_{7} = a_{1} \cdot r^{n - 1} = 38 \cdot {0.13157894736842105}^{7 - 1} = 38 \cdot {0.13157894736842105}^{6} = 38 \cdot 5.189415519713616 E - 06 = 0.0001971977897491174$

$a_{8} = a_{1} \cdot r^{n - 1} = 38 \cdot {0.13157894736842105}^{8 - 1} = 38 \cdot {0.13157894736842105}^{7} = 38 \cdot 6.828178315412652 E - 07 = 2.5947077598568078 E - 05$

$a_{9} = a_{1} \cdot r^{n - 1} = 38 \cdot {0.13157894736842105}^{9 - 1} = 38 \cdot {0.13157894736842105}^{8} = 38 \cdot 8.984445151858752 E - 08 = 3.414089157706326 E - 06$

$a_{10} = a_{1} \cdot r^{n - 1} = 38 \cdot {0.13157894736842105}^{10 - 1} = 38 \cdot {0.13157894736842105}^{9} = 38 \cdot 1.1821638357708883 E - 08 = 4.4922225759293755 E - 07$

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