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解答 - 几何数列

公比是：

r = 0.013157894736842105

r=0.013157894736842105

该系列的和是：

s = 1463

s=1463

此系列的通用形式是：

a_{n} = 1444 \cdot {0.013157894736842105}^{n - 1}

a_n=1444*0.013157894736842105^(n-1)

这个序列的第n项是：

1444, 19, 0.24999999999999997, 0.0032894736842105257, 4.328254847645429 E - 05, 5.695072167954511 E - 07, 7.493516010466462 E - 09, 9.85988948745587 E - 11, 1.2973538799284038 E - 12, 1.7070445788531627 E - 14

1444,19,0.24999999999999997,0.0032894736842105257,4.328254847645429E-05,5.695072167954511E-07,7.493516010466462E-09,9.85988948745587E-11,1.2973538799284038E-12,1.7070445788531627E-14

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：

$a_{2} a_{1} = \frac{19}{1444} = 0.013157894736842105$

该序列的公比（ $r$ ）保持不变，并且等于两个连续项的商。
$r = 0.013157894736842105$

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： $a = 1, 444$ 、公比： $r = 0.013157894736842105$ 和元素数目 $n = 2$ 插入几何级数求和公式：

$s_{2} = 1444 * ((1 - {0.013157894736842105}^{2}) / (1 - 0.013157894736842105))$

$s_{2} = 1444 * ((1 - 0.00017313019390581715) / (1 - 0.013157894736842105))$

$s_{2} = 1444 * (0.9998268698060941 / (1 - 0.013157894736842105))$

$s_{2} = 1444 * (0.9998268698060941 / 0.9868421052631579)$

$s_{2} = 1444 \cdot 1.013157894736842$

$s_{2} = 1463$

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： $a = 1, 444$ 和公比： $r = 0.013157894736842105$ 插入几何级数的公式：

$a_{n} = 1444 \cdot {0.013157894736842105}^{n - 1}$

4. 找到第n项

使用通用公式找到第n项

$a_{1} = 1444$

$a_{2} = a_{1} \cdot r^{n - 1} = 1444 \cdot {0.013157894736842105}^{2 - 1} = 1444 \cdot {0.013157894736842105}^{1} = 1444 \cdot 0.013157894736842105 = 19$

$a_{3} = a_{1} \cdot r^{n - 1} = 1444 \cdot {0.013157894736842105}^{3 - 1} = 1444 \cdot {0.013157894736842105}^{2} = 1444 \cdot 0.00017313019390581715 = 0.24999999999999997$

$a_{4} = a_{1} \cdot r^{n - 1} = 1444 \cdot {0.013157894736842105}^{4 - 1} = 1444 \cdot {0.013157894736842105}^{3} = 1444 \cdot 2.2780288671818044 E - 06 = 0.0032894736842105257$

$a_{5} = a_{1} \cdot r^{n - 1} = 1444 \cdot {0.013157894736842105}^{5 - 1} = 1444 \cdot {0.013157894736842105}^{4} = 1444 \cdot 2.997406404186585 E - 08 = 4.328254847645429 E - 05$

$a_{6} = a_{1} \cdot r^{n - 1} = 1444 \cdot {0.013157894736842105}^{6 - 1} = 1444 \cdot {0.013157894736842105}^{5} = 1444 \cdot 3.9439557949823484 E - 10 = 5.695072167954511 E - 07$

$a_{7} = a_{1} \cdot r^{n - 1} = 1444 \cdot {0.013157894736842105}^{7 - 1} = 1444 \cdot {0.013157894736842105}^{6} = 1444 \cdot 5.189415519713616 E - 12 = 7.493516010466462 E - 09$

$a_{8} = a_{1} \cdot r^{n - 1} = 1444 \cdot {0.013157894736842105}^{8 - 1} = 1444 \cdot {0.013157894736842105}^{7} = 1444 \cdot 6.828178315412652 E - 14 = 9.85988948745587 E - 11$

$a_{9} = a_{1} \cdot r^{n - 1} = 1444 \cdot {0.013157894736842105}^{9 - 1} = 1444 \cdot {0.013157894736842105}^{8} = 1444 \cdot 8.984445151858752 E - 16 = 1.2973538799284038 E - 12$

$a_{10} = a_{1} \cdot r^{n - 1} = 1444 \cdot {0.013157894736842105}^{10 - 1} = 1444 \cdot {0.013157894736842105}^{9} = 1444 \cdot 1.1821638357708884 E - 17 = 1.7070445788531627 E - 14$

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几何数列