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解答 - 几何数列

公比是：

r = 0.03167420814479638

r=0.03167420814479638

该系列的和是：

s = 2964

s=2964

此系列的通用形式是：

a_{n} = 2873 \cdot {0.03167420814479638}^{n - 1}

a_n=2873*0.03167420814479638^(n-1)

这个序列的第n项是：

2873, 91, 2.8823529411764706, 0.09129624700558955, 0.002891736330493786, 9.15934584319299 E - 05, 2.901150267074702 E - 06, 9.189163741865573 E - 08, 2.9105948503646608 E - 09, 9.219078711562274 E - 11

2873,91,2.8823529411764706,0.09129624700558955,0.002891736330493786,9.15934584319299E-05,2.901150267074702E-06,9.189163741865573E-08,2.9105948503646608E-09,9.219078711562274E-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：

$a_{2} a_{1} = \frac{91}{2873} = 0.03167420814479638$

该序列的公比（ $r$ ）保持不变，并且等于两个连续项的商。
$r = 0.03167420814479638$

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： $a = 2, 873$ 、公比： $r = 0.03167420814479638$ 和元素数目 $n = 2$ 插入几何级数求和公式：

$s_{2} = 2873 * ((1 - {0.03167420814479638}^{2}) / (1 - 0.03167420814479638))$

$s_{2} = 2873 * ((1 - 0.0010032554615998853) / (1 - 0.03167420814479638))$

$s_{2} = 2873 * (0.9989967445384001 / (1 - 0.03167420814479638))$

$s_{2} = 2873 * (0.9989967445384001 / 0.9683257918552036)$

$s_{2} = 2873 \cdot 1.0316742081447965$

$s_{2} = 2964.0000000000005$

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： $a = 2, 873$ 和公比： $r = 0.03167420814479638$ 插入几何级数的公式：

$a_{n} = 2873 \cdot {0.03167420814479638}^{n - 1}$

4. 找到第n项

使用通用公式找到第n项

$a_{1} = 2873$

$a_{2} = a_{1} \cdot r^{n - 1} = 2873 \cdot {0.03167420814479638}^{2 - 1} = 2873 \cdot {0.03167420814479638}^{1} = 2873 \cdot 0.03167420814479638 = 91$

$a_{3} = a_{1} \cdot r^{n - 1} = 2873 \cdot {0.03167420814479638}^{3 - 1} = 2873 \cdot {0.03167420814479638}^{2} = 2873 \cdot 0.0010032554615998853 = 2.8823529411764706$

$a_{4} = a_{1} \cdot r^{n - 1} = 2873 \cdot {0.03167420814479638}^{4 - 1} = 2873 \cdot {0.03167420814479638}^{3} = 2873 \cdot 3.1777322313118534 E - 05 = 0.09129624700558955$

$a_{5} = a_{1} \cdot r^{n - 1} = 2873 \cdot {0.03167420814479638}^{5 - 1} = 2873 \cdot {0.03167420814479638}^{4} = 2873 \cdot 1.0065215212299987 E - 06 = 0.002891736330493786$

$a_{6} = a_{1} \cdot r^{n - 1} = 2873 \cdot {0.03167420814479638}^{6 - 1} = 2873 \cdot {0.03167420814479638}^{5} = 2873 \cdot 3.188077216565607 E - 08 = 9.15934584319299 E - 05$

$a_{7} = a_{1} \cdot r^{n - 1} = 2873 \cdot {0.03167420814479638}^{7 - 1} = 2873 \cdot {0.03167420814479638}^{6} = 2873 \cdot 1.009798213391821 E - 09 = 2.901150267074702 E - 06$

$a_{8} = a_{1} \cdot r^{n - 1} = 2873 \cdot {0.03167420814479638}^{8 - 1} = 2873 \cdot {0.03167420814479638}^{7} = 2873 \cdot 3.1984558795216056 E - 11 = 9.189163741865573 E - 08$

$a_{9} = a_{1} \cdot r^{n - 1} = 2873 \cdot {0.03167420814479638}^{9 - 1} = 2873 \cdot {0.03167420814479638}^{8} = 2873 \cdot 1.013085572699151 E - 12 = 2.9105948503646608 E - 09$

$a_{10} = a_{1} \cdot r^{n - 1} = 2873 \cdot {0.03167420814479638}^{10 - 1} = 2873 \cdot {0.03167420814479638}^{9} = 2873 \cdot 3.208868329816315 E - 14 = 9.219078711562274 E - 11$

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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