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解答 - 几何数列

公比是：

r = 0.029411764705882353

r=0.029411764705882353

该系列的和是：

s = 2940

s=2940

此系列的通用形式是：

a_{n} = 2856 \cdot {0.029411764705882353}^{n - 1}

a_n=2856*0.029411764705882353^(n-1)

这个序列的第n项是：

2856, 84, 2.4705882352941178, 0.0726643598615917, 0.0021371870547526968, 6.285844278684403 E - 05, 1.8487777290248242 E - 06, 5.437581555955365 E - 08, 1.5992886929280485 E - 09, 4.70379027331779 E - 11

2856,84,2.4705882352941178,0.0726643598615917,0.0021371870547526968,6.285844278684403E-05,1.8487777290248242E-06,5.437581555955365E-08,1.5992886929280485E-09,4.70379027331779E-11

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：

$a_{2} a_{1} = \frac{84}{2856} = 0.029411764705882353$

该序列的公比（ $r$ ）保持不变，并且等于两个连续项的商。
$r = 0.029411764705882353$

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： $a = 2, 856$ 、公比： $r = 0.029411764705882353$ 和元素数目 $n = 2$ 插入几何级数求和公式：

$s_{2} = 2856 * ((1 - {0.029411764705882353}^{2}) / (1 - 0.029411764705882353))$

$s_{2} = 2856 * ((1 - 0.0008650519031141869) / (1 - 0.029411764705882353))$

$s_{2} = 2856 * (0.9991349480968859 / (1 - 0.029411764705882353))$

$s_{2} = 2856 * (0.9991349480968859 / 0.9705882352941176)$

$s_{2} = 2856 \cdot 1.0294117647058825$

$s_{2} = 2940.0000000000005$

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： $a = 2, 856$ 和公比： $r = 0.029411764705882353$ 插入几何级数的公式：

$a_{n} = 2856 \cdot {0.029411764705882353}^{n - 1}$

4. 找到第n项

使用通用公式找到第n项

$a_{1} = 2856$

$a_{2} = a_{1} \cdot r^{n - 1} = 2856 \cdot {0.029411764705882353}^{2 - 1} = 2856 \cdot {0.029411764705882353}^{1} = 2856 \cdot 0.029411764705882353 = 84$

$a_{3} = a_{1} \cdot r^{n - 1} = 2856 \cdot {0.029411764705882353}^{3 - 1} = 2856 \cdot {0.029411764705882353}^{2} = 2856 \cdot 0.0008650519031141869 = 2.4705882352941178$

$a_{4} = a_{1} \cdot r^{n - 1} = 2856 \cdot {0.029411764705882353}^{4 - 1} = 2856 \cdot {0.029411764705882353}^{3} = 2856 \cdot 2.54427030327702 E - 05 = 0.0726643598615917$

$a_{5} = a_{1} \cdot r^{n - 1} = 2856 \cdot {0.029411764705882353}^{5 - 1} = 2856 \cdot {0.029411764705882353}^{4} = 2856 \cdot 7.483147950814765 E - 07 = 0.0021371870547526968$

$a_{6} = a_{1} \cdot r^{n - 1} = 2856 \cdot {0.029411764705882353}^{6 - 1} = 2856 \cdot {0.029411764705882353}^{5} = 2856 \cdot 2.2009258678866955 E - 08 = 6.285844278684403 E - 05$

$a_{7} = a_{1} \cdot r^{n - 1} = 2856 \cdot {0.029411764705882353}^{7 - 1} = 2856 \cdot {0.029411764705882353}^{6} = 2856 \cdot 6.47331137613734 E - 10 = 1.8487777290248242 E - 06$

$a_{8} = a_{1} \cdot r^{n - 1} = 2856 \cdot {0.029411764705882353}^{8 - 1} = 2856 \cdot {0.029411764705882353}^{7} = 2856 \cdot 1.9039151106286292 E - 11 = 5.437581555955365 E - 08$

$a_{9} = a_{1} \cdot r^{n - 1} = 2856 \cdot {0.029411764705882353}^{9 - 1} = 2856 \cdot {0.029411764705882353}^{8} = 2856 \cdot 5.599750325378321 E - 13 = 1.5992886929280485 E - 09$

$a_{10} = a_{1} \cdot r^{n - 1} = 2856 \cdot {0.029411764705882353}^{10 - 1} = 2856 \cdot {0.029411764705882353}^{9} = 2856 \cdot 1.6469853898171533 E - 14 = 4.70379027331779 E - 11$

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几何序列常用于解释数学、物理、工程、生物、经济、计算机科学、金融等领域的概念，因此它们是我们工具箱中非常有用的工具。例如，几何序列最常见的应用之一就是计算已经获得或未付的复利，这是与金融相关的最常见活动之一，可能意味着赚取或失去大量的金钱！其他应用包括但不仅限于计算概率、测算随时间变化的放射性以及设计建筑物。

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几何数列