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 = 0.023622047244094488

r=0.023622047244094488

该系列的和是：

s = 130

s=130

此系列的通用形式是：

a_{n} = 127 \cdot {0.023622047244094488}^{n - 1}

a_n=127*0.023622047244094488^(n-1)

这个序列的第n项是：

127, 3, 0.07086614173228345, 0.0016740033480066958, 3.954338617338652 E - 05, 9.340957363792091 E - 07, 2.2065253615256907 E - 08, 5.212264633525253 E - 10, 1.2312436142185639 E - 11, 2.9084494824060565 E - 13

127,3,0.07086614173228345,0.0016740033480066958,3.954338617338652E-05,9.340957363792091E-07,2.2065253615256907E-08,5.212264633525253E-10,1.2312436142185639E-11,2.9084494824060565E-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：

$a_{2} a_{1} = \frac{3}{127} = 0.023622047244094488$

该序列的公比（ $r$ ）保持不变，并且等于两个连续项的商。
$r = 0.023622047244094488$

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： $a = 127$ 、公比： $r = 0.023622047244094488$ 和元素数目 $n = 2$ 插入几何级数求和公式：

$s_{2} = 127 * ((1 - {0.023622047244094488}^{2}) / (1 - 0.023622047244094488))$

$s_{2} = 127 * ((1 - 0.0005580011160022319) / (1 - 0.023622047244094488))$

$s_{2} = 127 * (0.9994419988839978 / (1 - 0.023622047244094488))$

$s_{2} = 127 * (0.9994419988839978 / 0.9763779527559056)$

$s_{2} = 127 \cdot 1.0236220472440944$

$s_{2} = 130$

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： $a = 127$ 和公比： $r = 0.023622047244094488$ 插入几何级数的公式：

$a_{n} = 127 \cdot {0.023622047244094488}^{n - 1}$

4. 找到第n项

使用通用公式找到第n项

$a_{1} = 127$

$a_{2} = a_{1} \cdot r^{n - 1} = 127 \cdot {0.023622047244094488}^{2 - 1} = 127 \cdot {0.023622047244094488}^{1} = 127 \cdot 0.023622047244094488 = 3$

$a_{3} = a_{1} \cdot r^{n - 1} = 127 \cdot {0.023622047244094488}^{3 - 1} = 127 \cdot {0.023622047244094488}^{2} = 127 \cdot 0.0005580011160022319 = 0.07086614173228345$

$a_{4} = a_{1} \cdot r^{n - 1} = 127 \cdot {0.023622047244094488}^{4 - 1} = 127 \cdot {0.023622047244094488}^{3} = 127 \cdot 1.3181128724462172 E - 05 = 0.0016740033480066958$

$a_{5} = a_{1} \cdot r^{n - 1} = 127 \cdot {0.023622047244094488}^{5 - 1} = 127 \cdot {0.023622047244094488}^{4} = 127 \cdot 3.1136524545973637 E - 07 = 3.954338617338652 E - 05$

$a_{6} = a_{1} \cdot r^{n - 1} = 127 \cdot {0.023622047244094488}^{6 - 1} = 127 \cdot {0.023622047244094488}^{5} = 127 \cdot 7.355084538418969 E - 09 = 9.340957363792091 E - 07$

$a_{7} = a_{1} \cdot r^{n - 1} = 127 \cdot {0.023622047244094488}^{7 - 1} = 127 \cdot {0.023622047244094488}^{6} = 127 \cdot 1.737421544508418 E - 10 = 2.2065253615256907 E - 08$

$a_{8} = a_{1} \cdot r^{n - 1} = 127 \cdot {0.023622047244094488}^{8 - 1} = 127 \cdot {0.023622047244094488}^{7} = 127 \cdot 4.104145380728546 E - 12 = 5.212264633525253 E - 10$

$a_{9} = a_{1} \cdot r^{n - 1} = 127 \cdot {0.023622047244094488}^{9 - 1} = 127 \cdot {0.023622047244094488}^{8} = 127 \cdot 9.694831608020188 E - 14 = 1.2312436142185639 E - 11$

$a_{10} = a_{1} \cdot r^{n - 1} = 127 \cdot {0.023622047244094488}^{10 - 1} = 127 \cdot {0.023622047244094488}^{9} = 127 \cdot 2.290117702681934 E - 15 = 2.9084494824060565 E - 13$

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