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解答 - 几何数列

公比是：

r = 0.006604812077370656

r=0.006604812077370656

该系列的和是：

s = 6401

s=6401

此系列的通用形式是：

a_{n} = 6359 \cdot {0.006604812077370656}^{n - 1}

a_n=6359*0.006604812077370656^(n-1)

这个序列的第n项是：

6359, 42, 0.27740210724956754, 0.0018321887882500134, 1.2101262636656797 E - 05, 7.992656561402508 E - 08, 5.27899945870271 E - 10, 3.4866799381272814 E - 12, 2.3028865765269042 E - 14, 1.5210133073459657 E - 16

6359,42,0.27740210724956754,0.0018321887882500134,1.2101262636656797E-05,7.992656561402508E-08,5.27899945870271E-10,3.4866799381272814E-12,2.3028865765269042E-14,1.5210133073459657E-16

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：

$a_{2} a_{1} = \frac{42}{6359} = 0.006604812077370656$

该序列的公比（ $r$ ）保持不变，并且等于两个连续项的商。
$r = 0.006604812077370656$

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： $a = 6, 359$ 、公比： $r = 0.006604812077370656$ 和元素数目 $n = 2$ 插入几何级数求和公式：

$s_{2} = 6359 * ((1 - {0.006604812077370656}^{2}) / (1 - 0.006604812077370656))$

$s_{2} = 6359 * ((1 - 4.362354257738128 E - 05) / (1 - 0.006604812077370656))$

$s_{2} = 6359 * (0.9999563764574226 / (1 - 0.006604812077370656))$

$s_{2} = 6359 * (0.9999563764574226 / 0.9933951879226294)$

$s_{2} = 6359 \cdot 1.0066048120773707$

$s_{2} = 6401.000000000001$

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： $a = 6, 359$ 和公比： $r = 0.006604812077370656$ 插入几何级数的公式：

$a_{n} = 6359 \cdot {0.006604812077370656}^{n - 1}$

4. 找到第n项

使用通用公式找到第n项

$a_{1} = 6359$

$a_{2} = a_{1} \cdot r^{n - 1} = 6359 \cdot {0.006604812077370656}^{2 - 1} = 6359 \cdot {0.006604812077370656}^{1} = 6359 \cdot 0.006604812077370656 = 42$

$a_{3} = a_{1} \cdot r^{n - 1} = 6359 \cdot {0.006604812077370656}^{3 - 1} = 6359 \cdot {0.006604812077370656}^{2} = 6359 \cdot 4.362354257738128 E - 05 = 0.27740210724956754$

$a_{4} = a_{1} \cdot r^{n - 1} = 6359 \cdot {0.006604812077370656}^{4 - 1} = 6359 \cdot {0.006604812077370656}^{3} = 6359 \cdot 2.8812530087278087 E - 07 = 0.0018321887882500134$

$a_{5} = a_{1} \cdot r^{n - 1} = 6359 \cdot {0.006604812077370656}^{5 - 1} = 6359 \cdot {0.006604812077370656}^{4} = 6359 \cdot 1.903013467000597 E - 09 = 1.2101262636656797 E - 05$

$a_{6} = a_{1} \cdot r^{n - 1} = 6359 \cdot {0.006604812077370656}^{6 - 1} = 6359 \cdot {0.006604812077370656}^{5} = 6359 \cdot 1.2569046330244548 E - 11 = 7.992656561402508 E - 08$

$a_{7} = a_{1} \cdot r^{n - 1} = 6359 \cdot {0.006604812077370656}^{7 - 1} = 6359 \cdot {0.006604812077370656}^{6} = 6359 \cdot 8.301618900303051 E - 14 = 5.27899945870271 E - 10$

$a_{8} = a_{1} \cdot r^{n - 1} = 6359 \cdot {0.006604812077370656}^{8 - 1} = 6359 \cdot {0.006604812077370656}^{7} = 6359 \cdot 5.483063277445009 E - 16 = 3.4866799381272814 E - 12$

$a_{9} = a_{1} \cdot r^{n - 1} = 6359 \cdot {0.006604812077370656}^{9 - 1} = 6359 \cdot {0.006604812077370656}^{8} = 6359 \cdot 3.621460255585633 E - 18 = 2.3028865765269042 E - 14$

$a_{10} = a_{1} \cdot r^{n - 1} = 6359 \cdot {0.006604812077370656}^{10 - 1} = 6359 \cdot {0.006604812077370656}^{9} = 6359 \cdot 2.391906443380981 E - 20 = 1.5210133073459657 E - 16$

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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