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解答 - 几何数列

公比是：

r = 0.005791505791505791

r=0.005791505791505791

该系列的和是：

s = 521

s=521

此系列的通用形式是：

a_{n} = 518 \cdot {0.005791505791505791}^{n - 1}

a_n=518*0.005791505791505791^(n-1)

这个序列的第n项是：

518, 3, 0.01737451737451737, 0.00010062461799913536, 5.827680579100503 E - 07, 3.3751045824906385 E - 09, 1.954693773643227 E - 11, 1.1320620310675059 E - 13, 6.556343809271269 E - 16, 3.79711031424977 E - 18

518,3,0.01737451737451737,0.00010062461799913536,5.827680579100503E-07,3.3751045824906385E-09,1.954693773643227E-11,1.1320620310675059E-13,6.556343809271269E-16,3.79711031424977E-18

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：

$a_{2} a_{1} = \frac{3}{518} = 0.005791505791505791$

该序列的公比（ $r$ ）保持不变，并且等于两个连续项的商。
$r = 0.005791505791505791$

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： $a = 518$ 、公比： $r = 0.005791505791505791$ 和元素数目 $n = 2$ 插入几何级数求和公式：

$s_{2} = 518 * ((1 - {0.005791505791505791}^{2}) / (1 - 0.005791505791505791))$

$s_{2} = 518 * ((1 - 3.354153933304512 E - 05) / (1 - 0.005791505791505791))$

$s_{2} = 518 * (0.999966458460667 / (1 - 0.005791505791505791))$

$s_{2} = 518 * (0.999966458460667 / 0.9942084942084942)$

$s_{2} = 518 \cdot 1.005791505791506$

$s_{2} = 521$

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： $a = 518$ 和公比： $r = 0.005791505791505791$ 插入几何级数的公式：

$a_{n} = 518 \cdot {0.005791505791505791}^{n - 1}$

4. 找到第n项

使用通用公式找到第n项

$a_{1} = 518$

$a_{2} = a_{1} \cdot r^{n - 1} = 518 \cdot {0.005791505791505791}^{2 - 1} = 518 \cdot {0.005791505791505791}^{1} = 518 \cdot 0.005791505791505791 = 3$

$a_{3} = a_{1} \cdot r^{n - 1} = 518 \cdot {0.005791505791505791}^{3 - 1} = 518 \cdot {0.005791505791505791}^{2} = 518 \cdot 3.354153933304512 E - 05 = 0.01737451737451737$

$a_{4} = a_{1} \cdot r^{n - 1} = 518 \cdot {0.005791505791505791}^{4 - 1} = 518 \cdot {0.005791505791505791}^{3} = 518 \cdot 1.942560193033501 E - 07 = 0.00010062461799913536$

$a_{5} = a_{1} \cdot r^{n - 1} = 518 \cdot {0.005791505791505791}^{5 - 1} = 518 \cdot {0.005791505791505791}^{4} = 518 \cdot 1.125034860830213 E - 09 = 5.827680579100503 E - 07$

$a_{6} = a_{1} \cdot r^{n - 1} = 518 \cdot {0.005791505791505791}^{6 - 1} = 518 \cdot {0.005791505791505791}^{5} = 518 \cdot 6.51564591214409 E - 12 = 3.3751045824906385 E - 09$

$a_{7} = a_{1} \cdot r^{n - 1} = 518 \cdot {0.005791505791505791}^{7 - 1} = 518 \cdot {0.005791505791505791}^{6} = 518 \cdot 3.7735401035583534 E - 14 = 1.954693773643227 E - 11$

$a_{8} = a_{1} \cdot r^{n - 1} = 518 \cdot {0.005791505791505791}^{8 - 1} = 518 \cdot {0.005791505791505791}^{7} = 518 \cdot 2.1854479364237565 E - 16 = 1.1320620310675059 E - 13$

$a_{9} = a_{1} \cdot r^{n - 1} = 518 \cdot {0.005791505791505791}^{9 - 1} = 518 \cdot {0.005791505791505791}^{8} = 518 \cdot 1.2657034380832566 E - 18 = 6.556343809271269 E - 16$

$a_{10} = a_{1} \cdot r^{n - 1} = 518 \cdot {0.005791505791505791}^{10 - 1} = 518 \cdot {0.005791505791505791}^{9} = 518 \cdot 7.330328791987972 E - 21 = 3.79711031424977 E - 18$

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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