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 = 0.36363636363636365

r=0.36363636363636365

该系列的和是：

s = 45

s=45

此系列的通用形式是：

a_{n} = 33 \cdot {0.36363636363636365}^{n - 1}

a_n=33*0.36363636363636365^(n-1)

这个序列的第n项是：

33, 12, 4.363636363636363, 1.5867768595041323, 0.5770097670924118, 0.20982173348814973, 0.076298812177509, 0.027745022610003275, 0.010089099130910282, 0.0036687633203310115

33,12,4.363636363636363,1.5867768595041323,0.5770097670924118,0.20982173348814973,0.076298812177509,0.027745022610003275,0.010089099130910282,0.0036687633203310115

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：

$a_{2} a_{1} = \frac{12}{33} = 0.36363636363636365$

该序列的公比（ $r$ ）保持不变，并且等于两个连续项的商。
$r = 0.36363636363636365$

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： $a = 33$ 、公比： $r = 0.36363636363636365$ 和元素数目 $n = 2$ 插入几何级数求和公式：

$s_{2} = 33 * ((1 - {0.36363636363636365}^{2}) / (1 - 0.36363636363636365))$

$s_{2} = 33 * ((1 - 0.1322314049586777) / (1 - 0.36363636363636365))$

$s_{2} = 33 * (0.8677685950413223 / (1 - 0.36363636363636365))$

$s_{2} = 33 * (0.8677685950413223 / 0.6363636363636364)$

$s_{2} = 33 \cdot 1.3636363636363638$

$s_{2} = 45.00000000000001$

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： $a = 33$ 和公比： $r = 0.36363636363636365$ 插入几何级数的公式：

$a_{n} = 33 \cdot {0.36363636363636365}^{n - 1}$

4. 找到第n项

使用通用公式找到第n项

$a_{1} = 33$

$a_{2} = a_{1} \cdot r^{n - 1} = 33 \cdot {0.36363636363636365}^{2 - 1} = 33 \cdot {0.36363636363636365}^{1} = 33 \cdot 0.36363636363636365 = 12$

$a_{3} = a_{1} \cdot r^{n - 1} = 33 \cdot {0.36363636363636365}^{3 - 1} = 33 \cdot {0.36363636363636365}^{2} = 33 \cdot 0.1322314049586777 = 4.363636363636363$

$a_{4} = a_{1} \cdot r^{n - 1} = 33 \cdot {0.36363636363636365}^{4 - 1} = 33 \cdot {0.36363636363636365}^{3} = 33 \cdot 0.04808414725770098 = 1.5867768595041323$

$a_{5} = a_{1} \cdot r^{n - 1} = 33 \cdot {0.36363636363636365}^{5 - 1} = 33 \cdot {0.36363636363636365}^{4} = 33 \cdot 0.01748514445734581 = 0.5770097670924118$

$a_{6} = a_{1} \cdot r^{n - 1} = 33 \cdot {0.36363636363636365}^{6 - 1} = 33 \cdot {0.36363636363636365}^{5} = 33 \cdot 0.0063582343481257495 = 0.20982173348814973$

$a_{7} = a_{1} \cdot r^{n - 1} = 33 \cdot {0.36363636363636365}^{7 - 1} = 33 \cdot {0.36363636363636365}^{6} = 33 \cdot 0.0023120852175002727 = 0.076298812177509$

$a_{8} = a_{1} \cdot r^{n - 1} = 33 \cdot {0.36363636363636365}^{8 - 1} = 33 \cdot {0.36363636363636365}^{7} = 33 \cdot 0.0008407582609091901 = 0.027745022610003275$

$a_{9} = a_{1} \cdot r^{n - 1} = 33 \cdot {0.36363636363636365}^{9 - 1} = 33 \cdot {0.36363636363636365}^{8} = 33 \cdot 0.00030573027669425094 = 0.010089099130910282$

$a_{10} = a_{1} \cdot r^{n - 1} = 33 \cdot {0.36363636363636365}^{10 - 1} = 33 \cdot {0.36363636363636365}^{9} = 33 \cdot 0.00011117464607063672 = 0.0036687633203310115$

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