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 = 1.0526315789473684

r=1.0526315789473684

该系列的和是：

s = 77

s=77

此系列的通用形式是：

a_{n} = 38 \cdot {1.0526315789473684}^{n - 1}

a_n=38*1.0526315789473684^(n-1)

这个序列的第n项是：

38, 40, 42.10526315789473, 44.32132963988919, 46.654031199883356, 49.109506526193, 51.69421739599263, 54.41496567999224, 57.278911242097095, 60.293590781154826

38,40,42.10526315789473,44.32132963988919,46.654031199883356,49.109506526193,51.69421739599263,54.41496567999224,57.278911242097095,60.293590781154826

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：

$a_{2} a_{1} = \frac{40}{38} = 1.0526315789473684$

该序列的公比（ $r$ ）保持不变，并且等于两个连续项的商。
$r = 1.0526315789473684$

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： $a = 38$ 、公比： $r = 1.0526315789473684$ 和元素数目 $n = 2$ 插入几何级数求和公式：

$s_{2} = 38 * ((1 - {1.0526315789473684}^{2}) / (1 - 1.0526315789473684))$

$s_{2} = 38 * ((1 - 1.1080332409972298) / (1 - 1.0526315789473684))$

$s_{2} = 38 * (- 0.10803324099722977 / (1 - 1.0526315789473684))$

$s_{2} = 38 * (- 0.10803324099722977 / - 0.05263157894736836)$

$s_{2} = 38 \cdot 2.052631578947368$

$s_{2} = 77.99999999999999$

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： $a = 38$ 和公比： $r = 1.0526315789473684$ 插入几何级数的公式：

$a_{n} = 38 \cdot {1.0526315789473684}^{n - 1}$

4. 找到第n项

使用通用公式找到第n项

$a_{1} = 38$

$a_{2} = a_{1} \cdot r^{n - 1} = 38 \cdot {1.0526315789473684}^{2 - 1} = 38 \cdot {1.0526315789473684}^{1} = 38 \cdot 1.0526315789473684 = 40$

$a_{3} = a_{1} \cdot r^{n - 1} = 38 \cdot {1.0526315789473684}^{3 - 1} = 38 \cdot {1.0526315789473684}^{2} = 38 \cdot 1.1080332409972298 = 42.10526315789473$

$a_{4} = a_{1} \cdot r^{n - 1} = 38 \cdot {1.0526315789473684}^{4 - 1} = 38 \cdot {1.0526315789473684}^{3} = 38 \cdot 1.166350779997084 = 44.32132963988919$

$a_{5} = a_{1} \cdot r^{n - 1} = 38 \cdot {1.0526315789473684}^{5 - 1} = 38 \cdot {1.0526315789473684}^{4} = 38 \cdot 1.2277376631548251 = 46.654031199883356$

$a_{6} = a_{1} \cdot r^{n - 1} = 38 \cdot {1.0526315789473684}^{6 - 1} = 38 \cdot {1.0526315789473684}^{5} = 38 \cdot 1.2923554348998159 = 49.109506526193$

$a_{7} = a_{1} \cdot r^{n - 1} = 38 \cdot {1.0526315789473684}^{7 - 1} = 38 \cdot {1.0526315789473684}^{6} = 38 \cdot 1.360374141999806 = 51.69421739599263$

$a_{8} = a_{1} \cdot r^{n - 1} = 38 \cdot {1.0526315789473684}^{8 - 1} = 38 \cdot {1.0526315789473684}^{7} = 38 \cdot 1.4319727810524274 = 54.41496567999224$

$a_{9} = a_{1} \cdot r^{n - 1} = 38 \cdot {1.0526315789473684}^{9 - 1} = 38 \cdot {1.0526315789473684}^{8} = 38 \cdot 1.5073397695288708 = 57.278911242097095$

$a_{10} = a_{1} \cdot r^{n - 1} = 38 \cdot {1.0526315789473684}^{10 - 1} = 38 \cdot {1.0526315789473684}^{9} = 38 \cdot 1.5866734416093375 = 60.293590781154826$

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