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解答 - 几何数列

公比是：

r = 0.017699115044247787

r=0.017699115044247787

该系列的和是：

s = 1955

s=1955

此系列的通用形式是：

a_{n} = 1921 \cdot {0.017699115044247787}^{n - 1}

a_n=1921*0.017699115044247787^(n-1)

这个序列的第n项是：

1921, 34, 0.6017699115044247, 0.010650794893883623, 0.00018850964413953317, 3.3364538785758083 E - 06, 5.9052281036739967 E - 08, 1.0451731156945128 E - 09, 1.8498639215832082 E - 11, 3.274095436430457 E - 13

1921,34,0.6017699115044247,0.010650794893883623,0.00018850964413953317,3.3364538785758083E-06,5.9052281036739967E-08,1.0451731156945128E-09,1.8498639215832082E-11,3.274095436430457E-13

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：

$a_{2} a_{1} = \frac{34}{1921} = 0.017699115044247787$

该序列的公比（ $r$ ）保持不变，并且等于两个连续项的商。
$r = 0.017699115044247787$

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： $a = 1, 921$ 、公比： $r = 0.017699115044247787$ 和元素数目 $n = 2$ 插入几何级数求和公式：

$s_{2} = 1921 * ((1 - {0.017699115044247787}^{2}) / (1 - 0.017699115044247787))$

$s_{2} = 1921 * ((1 - 0.00031325867334951836) / (1 - 0.017699115044247787))$

$s_{2} = 1921 * (0.9996867413266505 / (1 - 0.017699115044247787))$

$s_{2} = 1921 * (0.9996867413266505 / 0.9823008849557522)$

$s_{2} = 1921 \cdot 1.0176991150442478$

$s_{2} = 1955$

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： $a = 1, 921$ 和公比： $r = 0.017699115044247787$ 插入几何级数的公式：

$a_{n} = 1921 \cdot {0.017699115044247787}^{n - 1}$

4. 找到第n项

使用通用公式找到第n项

$a_{1} = 1921$

$a_{2} = a_{1} \cdot r^{n - 1} = 1921 \cdot {0.017699115044247787}^{2 - 1} = 1921 \cdot {0.017699115044247787}^{1} = 1921 \cdot 0.017699115044247787 = 34$

$a_{3} = a_{1} \cdot r^{n - 1} = 1921 \cdot {0.017699115044247787}^{3 - 1} = 1921 \cdot {0.017699115044247787}^{2} = 1921 \cdot 0.00031325867334951836 = 0.6017699115044247$

$a_{4} = a_{1} \cdot r^{n - 1} = 1921 \cdot {0.017699115044247787}^{4 - 1} = 1921 \cdot {0.017699115044247787}^{3} = 1921 \cdot 5.5444012982215636 E - 06 = 0.010650794893883623$

$a_{5} = a_{1} \cdot r^{n - 1} = 1921 \cdot {0.017699115044247787}^{5 - 1} = 1921 \cdot {0.017699115044247787}^{4} = 1921 \cdot 9.813099642870024 E - 08 = 0.00018850964413953317$

$a_{6} = a_{1} \cdot r^{n - 1} = 1921 \cdot {0.017699115044247787}^{6 - 1} = 1921 \cdot {0.017699115044247787}^{5} = 1921 \cdot 1.7368317951982344 E - 09 = 3.3364538785758083 E - 06$

$a_{7} = a_{1} \cdot r^{n - 1} = 1921 \cdot {0.017699115044247787}^{7 - 1} = 1921 \cdot {0.017699115044247787}^{6} = 1921 \cdot 3.074038575572096 E - 11 = 5.9052281036739967 E - 08$

$a_{8} = a_{1} \cdot r^{n - 1} = 1921 \cdot {0.017699115044247787}^{8 - 1} = 1921 \cdot {0.017699115044247787}^{7} = 1921 \cdot 5.440776239950613 E - 13 = 1.0451731156945128 E - 09$

$a_{9} = a_{1} \cdot r^{n - 1} = 1921 \cdot {0.017699115044247787}^{9 - 1} = 1921 \cdot {0.017699115044247787}^{8} = 1921 \cdot 9.629692460089579 E - 15 = 1.8498639215832082 E - 11$

$a_{10} = a_{1} \cdot r^{n - 1} = 1921 \cdot {0.017699115044247787}^{10 - 1} = 1921 \cdot {0.017699115044247787}^{9} = 1921 \cdot 1.7043703469185097 E - 16 = 3.274095436430457 E - 13$

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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