输入一个方程或问题

无法识别摄像头输入！

解答 - 几何数列

公比是：

r = 0.12021857923497267

r=0.12021857923497267

该系列的和是：

s = 15170

s=15170

此系列的通用形式是：

a_{n} = 13542 \cdot {0.12021857923497267}^{n - 1}

a_n=13542*0.12021857923497267^(n-1)

这个序列的第n项是：

13542, 1628, 195.7158469945355, 23.528681059452353, 2.8285846082401735, 0.3400484228485455, 0.04088013826594535, 0.004914552141261189, 0.0005908204759986129, 7.102759820748352 E - 05

13542,1628,195.7158469945355,23.528681059452353,2.8285846082401735,0.3400484228485455,0.04088013826594535,0.004914552141261189,0.0005908204759986129,7.102759820748352E-05

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：

$a_{2} a_{1} = \frac{1628}{13542} = 0.12021857923497267$

该序列的公比（ $r$ ）保持不变，并且等于两个连续项的商。
$r = 0.12021857923497267$

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： $a = 13, 542$ 、公比： $r = 0.12021857923497267$ 和元素数目 $n = 2$ 插入几何级数求和公式：

$s_{2} = 13542 * ((1 - {0.12021857923497267}^{2}) / (1 - 0.12021857923497267))$

$s_{2} = 13542 * ((1 - 0.014452506793275402) / (1 - 0.12021857923497267))$

$s_{2} = 13542 * (0.9855474932067246 / (1 - 0.12021857923497267))$

$s_{2} = 13542 * (0.9855474932067246 / 0.8797814207650273)$

$s_{2} = 13542 \cdot 1.1202185792349728$

$s_{2} = 15170.000000000002$

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： $a = 13, 542$ 和公比： $r = 0.12021857923497267$ 插入几何级数的公式：

$a_{n} = 13542 \cdot {0.12021857923497267}^{n - 1}$

4. 找到第n项

使用通用公式找到第n项

$a_{1} = 13542$

$a_{2} = a_{1} \cdot r^{n - 1} = 13542 \cdot {0.12021857923497267}^{2 - 1} = 13542 \cdot {0.12021857923497267}^{1} = 13542 \cdot 0.12021857923497267 = 1628$

$a_{3} = a_{1} \cdot r^{n - 1} = 13542 \cdot {0.12021857923497267}^{3 - 1} = 13542 \cdot {0.12021857923497267}^{2} = 13542 \cdot 0.014452506793275402 = 195.7158469945355$

$a_{4} = a_{1} \cdot r^{n - 1} = 13542 \cdot {0.12021857923497267}^{4 - 1} = 13542 \cdot {0.12021857923497267}^{3} = 13542 \cdot 0.0017374598330713597 = 23.528681059452353$

$a_{5} = a_{1} \cdot r^{n - 1} = 13542 \cdot {0.12021857923497267}^{5 - 1} = 13542 \cdot {0.12021857923497267}^{4} = 13542 \cdot 0.00020887495260967165 = 2.8285846082401735$

$a_{6} = a_{1} \cdot r^{n - 1} = 13542 \cdot {0.12021857923497267}^{6 - 1} = 13542 \cdot {0.12021857923497267}^{5} = 13542 \cdot 2.5110650040506975 E - 05 = 0.3400484228485455$

$a_{7} = a_{1} \cdot r^{n - 1} = 13542 \cdot {0.12021857923497267}^{7 - 1} = 13542 \cdot {0.12021857923497267}^{6} = 13542 \cdot 3.0187666715363575 E - 06 = 0.04088013826594535$

$a_{8} = a_{1} \cdot r^{n - 1} = 13542 \cdot {0.12021857923497267}^{8 - 1} = 13542 \cdot {0.12021857923497267}^{7} = 13542 \cdot 3.629118402939883 E - 07 = 0.004914552141261189$

$a_{9} = a_{1} \cdot r^{n - 1} = 13542 \cdot {0.12021857923497267}^{9 - 1} = 13542 \cdot {0.12021857923497267}^{8} = 13542 \cdot 4.362874582769258 E - 08 = 0.0005908204759986129$

$a_{10} = a_{1} \cdot r^{n - 1} = 13542 \cdot {0.12021857923497267}^{10 - 1} = 13542 \cdot {0.12021857923497267}^{9} = 13542 \cdot 5.244985837208944 E - 09 = 7.102759820748352 E - 05$

我们做得怎么样？

给我们反馈

为什么学习这个

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。

术语和主题

几何数列