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 = 0.2727272727272727

r=0.2727272727272727

该系列的和是：

s = 154

s=154

此系列的通用形式是：

a_{n} = 121 \cdot {0.2727272727272727}^{n - 1}

a_n=121*0.2727272727272727^(n-1)

这个序列的第n项是：

121, 33, 8.999999999999998, 2.4545454545454537, 0.6694214876033057, 0.1825694966190833, 0.049791680896113626, 0.013579549335303717, 0.0037035134550828315, 0.0010100491241134995

121,33,8.999999999999998,2.4545454545454537,0.6694214876033057,0.1825694966190833,0.049791680896113626,0.013579549335303717,0.0037035134550828315,0.0010100491241134995

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：

$a_{2} a_{1} = \frac{33}{121} = 0.2727272727272727$

该序列的公比（ $r$ ）保持不变，并且等于两个连续项的商。
$r = 0.2727272727272727$

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： $a = 121$ 、公比： $r = 0.2727272727272727$ 和元素数目 $n = 2$ 插入几何级数求和公式：

$s_{2} = 121 * ((1 - {0.2727272727272727}^{2}) / (1 - 0.2727272727272727))$

$s_{2} = 121 * ((1 - 0.07438016528925619) / (1 - 0.2727272727272727))$

$s_{2} = 121 * (0.9256198347107438 / (1 - 0.2727272727272727))$

$s_{2} = 121 * (0.9256198347107438 / 0.7272727272727273)$

$s_{2} = 121 \cdot 1.2727272727272727$

$s_{2} = 154$

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： $a = 121$ 和公比： $r = 0.2727272727272727$ 插入几何级数的公式：

$a_{n} = 121 \cdot {0.2727272727272727}^{n - 1}$

4. 找到第n项

使用通用公式找到第n项

$a_{1} = 121$

$a_{2} = a_{1} \cdot r^{n - 1} = 121 \cdot {0.2727272727272727}^{2 - 1} = 121 \cdot {0.2727272727272727}^{1} = 121 \cdot 0.2727272727272727 = 33$

$a_{3} = a_{1} \cdot r^{n - 1} = 121 \cdot {0.2727272727272727}^{3 - 1} = 121 \cdot {0.2727272727272727}^{2} = 121 \cdot 0.07438016528925619 = 8.999999999999998$

$a_{4} = a_{1} \cdot r^{n - 1} = 121 \cdot {0.2727272727272727}^{4 - 1} = 121 \cdot {0.2727272727272727}^{3} = 121 \cdot 0.020285499624342593 = 2.4545454545454537$

$a_{5} = a_{1} \cdot r^{n - 1} = 121 \cdot {0.2727272727272727}^{5 - 1} = 121 \cdot {0.2727272727272727}^{4} = 121 \cdot 0.005532408988457071 = 0.6694214876033057$

$a_{6} = a_{1} \cdot r^{n - 1} = 121 \cdot {0.2727272727272727}^{6 - 1} = 121 \cdot {0.2727272727272727}^{5} = 121 \cdot 0.0015088388150337464 = 0.1825694966190833$

$a_{7} = a_{1} \cdot r^{n - 1} = 121 \cdot {0.2727272727272727}^{7 - 1} = 121 \cdot {0.2727272727272727}^{6} = 121 \cdot 0.00041150149500920354 = 0.049791680896113626$

$a_{8} = a_{1} \cdot r^{n - 1} = 121 \cdot {0.2727272727272727}^{8 - 1} = 121 \cdot {0.2727272727272727}^{7} = 121 \cdot 0.00011222768045705551 = 0.013579549335303717$

$a_{9} = a_{1} \cdot r^{n - 1} = 121 \cdot {0.2727272727272727}^{9 - 1} = 121 \cdot {0.2727272727272727}^{8} = 121 \cdot 3.060754921556059 E - 05 = 0.0037035134550828315$

$a_{10} = a_{1} \cdot r^{n - 1} = 121 \cdot {0.2727272727272727}^{10 - 1} = 121 \cdot {0.2727272727272727}^{9} = 121 \cdot 8.347513422425615 E - 06 = 0.0010100491241134995$

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