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 = 0.2601626016260163

r=0.2601626016260163

该系列的和是：

s = 155

s=155

此系列的通用形式是：

a_{n} = 123 \cdot {0.2601626016260163}^{n - 1}

a_n=123*0.2601626016260163^(n-1)

这个序列的第n项是：

123, 32, 8.325203252032521, 2.1659065371141524, 0.5634878795744137, 0.1465984727348068, 0.03813944006108796, 0.009922455950852152, 0.002581451954693243, 0.0006715972565055593

123,32,8.325203252032521,2.1659065371141524,0.5634878795744137,0.1465984727348068,0.03813944006108796,0.009922455950852152,0.002581451954693243,0.0006715972565055593

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：

$a_{2} a_{1} = \frac{32}{123} = 0.2601626016260163$

该序列的公比（ $r$ ）保持不变，并且等于两个连续项的商。
$r = 0.2601626016260163$

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： $a = 123$ 、公比： $r = 0.2601626016260163$ 和元素数目 $n = 2$ 插入几何级数求和公式：

$s_{2} = 123 * ((1 - {0.2601626016260163}^{2}) / (1 - 0.2601626016260163))$

$s_{2} = 123 * ((1 - 0.06768457928481725) / (1 - 0.2601626016260163))$

$s_{2} = 123 * (0.9323154207151827 / (1 - 0.2601626016260163))$

$s_{2} = 123 * (0.9323154207151827 / 0.7398373983739837)$

$s_{2} = 123 \cdot 1.2601626016260163$

$s_{2} = 155$

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： $a = 123$ 和公比： $r = 0.2601626016260163$ 插入几何级数的公式：

$a_{n} = 123 \cdot {0.2601626016260163}^{n - 1}$

4. 找到第n项

使用通用公式找到第n项

$a_{1} = 123$

$a_{2} = a_{1} \cdot r^{n - 1} = 123 \cdot {0.2601626016260163}^{2 - 1} = 123 \cdot {0.2601626016260163}^{1} = 123 \cdot 0.2601626016260163 = 32$

$a_{3} = a_{1} \cdot r^{n - 1} = 123 \cdot {0.2601626016260163}^{3 - 1} = 123 \cdot {0.2601626016260163}^{2} = 123 \cdot 0.06768457928481725 = 8.325203252032521$

$a_{4} = a_{1} \cdot r^{n - 1} = 123 \cdot {0.2601626016260163}^{4 - 1} = 123 \cdot {0.2601626016260163}^{3} = 123 \cdot 0.017608996236700425 = 2.1659065371141524$

$a_{5} = a_{1} \cdot r^{n - 1} = 123 \cdot {0.2601626016260163}^{5 - 1} = 123 \cdot {0.2601626016260163}^{4} = 123 \cdot 0.004581202272962713 = 0.5634878795744137$

$a_{6} = a_{1} \cdot r^{n - 1} = 123 \cdot {0.2601626016260163}^{6 - 1} = 123 \cdot {0.2601626016260163}^{5} = 123 \cdot 0.0011918575019089985 = 0.1465984727348068$

$a_{7} = a_{1} \cdot r^{n - 1} = 123 \cdot {0.2601626016260163}^{7 - 1} = 123 \cdot {0.2601626016260163}^{6} = 123 \cdot 0.00031007674846412976 = 0.03813944006108796$

$a_{8} = a_{1} \cdot r^{n - 1} = 123 \cdot {0.2601626016260163}^{8 - 1} = 123 \cdot {0.2601626016260163}^{7} = 123 \cdot 8.067037358416385 E - 05 = 0.009922455950852152$

$a_{9} = a_{1} \cdot r^{n - 1} = 123 \cdot {0.2601626016260163}^{9 - 1} = 123 \cdot {0.2601626016260163}^{8} = 123 \cdot 2.0987414265798725 E - 05 = 0.002581451954693243$

$a_{10} = a_{1} \cdot r^{n - 1} = 123 \cdot {0.2601626016260163}^{10 - 1} = 123 \cdot {0.2601626016260163}^{9} = 123 \cdot 5.460140296793165 E - 06 = 0.0006715972565055593$

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