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解答 - 几何数列

公比是：

r = 0.05263157894736842

r=0.05263157894736842

该系列的和是：

s = 40

s=40

此系列的通用形式是：

a_{n} = 38 \cdot {0.05263157894736842}^{n - 1}

a_n=38*0.05263157894736842^(n-1)

这个序列的第n项是：

38, 2, 0.10526315789473682, 0.005540166204986149, 0.00029158769499927097, 1.5346720789435315 E - 05, 8.077221468123849 E - 07, 4.2511691937493936 E - 08, 2.2374574703944174 E - 09, 1.1776091949444303 E - 10

38,2,0.10526315789473682,0.005540166204986149,0.00029158769499927097,1.5346720789435315E-05,8.077221468123849E-07,4.2511691937493936E-08,2.2374574703944174E-09,1.1776091949444303E-10

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：

$a_{2} a_{1} = \frac{2}{38} = 0.05263157894736842$

该序列的公比（ $r$ ）保持不变，并且等于两个连续项的商。
$r = 0.05263157894736842$

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： $r = 0.05263157894736842$ 和元素数目 $n = 2$ 插入几何级数求和公式：

$s_{2} = 38 * ((1 - {0.05263157894736842}^{2}) / (1 - 0.05263157894736842))$

$s_{2} = 38 * ((1 - 0.0027700831024930744) / (1 - 0.05263157894736842))$

$s_{2} = 38 * (0.997229916897507 / (1 - 0.05263157894736842))$

$s_{2} = 38 * (0.997229916897507 / 0.9473684210526316)$

$s_{2} = 38 \cdot 1.0526315789473684$

$s_{2} = 40$

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： $r = 0.05263157894736842$ 插入几何级数的公式：

$a_{n} = 38 \cdot {0.05263157894736842}^{n - 1}$

4. 找到第n项

使用通用公式找到第n项

$a_{1} = 38$

$a_{2} = a_{1} \cdot r^{n - 1} = 38 \cdot {0.05263157894736842}^{2 - 1} = 38 \cdot {0.05263157894736842}^{1} = 38 \cdot 0.05263157894736842 = 2$

$a_{3} = a_{1} \cdot r^{n - 1} = 38 \cdot {0.05263157894736842}^{3 - 1} = 38 \cdot {0.05263157894736842}^{2} = 38 \cdot 0.0027700831024930744 = 0.10526315789473682$

$a_{4} = a_{1} \cdot r^{n - 1} = 38 \cdot {0.05263157894736842}^{4 - 1} = 38 \cdot {0.05263157894736842}^{3} = 38 \cdot 0.00014579384749963548 = 0.005540166204986149$

$a_{5} = a_{1} \cdot r^{n - 1} = 38 \cdot {0.05263157894736842}^{5 - 1} = 38 \cdot {0.05263157894736842}^{4} = 38 \cdot 7.673360394717657 E - 06 = 0.00029158769499927097$

$a_{6} = a_{1} \cdot r^{n - 1} = 38 \cdot {0.05263157894736842}^{6 - 1} = 38 \cdot {0.05263157894736842}^{5} = 38 \cdot 4.0386107340619247 E - 07 = 1.5346720789435315 E - 05$

$a_{7} = a_{1} \cdot r^{n - 1} = 38 \cdot {0.05263157894736842}^{7 - 1} = 38 \cdot {0.05263157894736842}^{6} = 38 \cdot 2.125584596874697 E - 08 = 8.077221468123849 E - 07$

$a_{8} = a_{1} \cdot r^{n - 1} = 38 \cdot {0.05263157894736842}^{8 - 1} = 38 \cdot {0.05263157894736842}^{7} = 38 \cdot 1.118728735197209 E - 09 = 4.2511691937493936 E - 08$

$a_{9} = a_{1} \cdot r^{n - 1} = 38 \cdot {0.05263157894736842}^{9 - 1} = 38 \cdot {0.05263157894736842}^{8} = 38 \cdot 5.888045974722152 E - 11 = 2.2374574703944174 E - 09$

$a_{10} = a_{1} \cdot r^{n - 1} = 38 \cdot {0.05263157894736842}^{10 - 1} = 38 \cdot {0.05263157894736842}^{9} = 38 \cdot 3.0989715656432376 E - 12 = 1.1776091949444303 E - 10$

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几何数列