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 = 0.2992905153099328

r=0.2992905153099328

该系列的和是：

s = 6959

s=6959

此系列的通用形式是：

a_{n} = 5356 \cdot {0.2992905153099328}^{n - 1}

a_n=5356*0.2992905153099328^(n-1)

这个序列的第n项是：

5356, 1603, 479.76269604182227, 143.5884245248396, 42.97465356858064, 12.861906211806343, 3.8494465379995453, 1.1521028380159208, 0.3448134520798209, 0.10319939575876642

5356,1603,479.76269604182227,143.5884245248396,42.97465356858064,12.861906211806343,3.8494465379995453,1.1521028380159208,0.3448134520798209,0.10319939575876642

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：

$a_{2} a_{1} = \frac{1603}{5356} = 0.2992905153099328$

该序列的公比（ $r$ ）保持不变，并且等于两个连续项的商。
$r = 0.2992905153099328$

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： $a = 5, 356$ 、公比： $r = 0.2992905153099328$ 和元素数目 $n = 2$ 插入几何级数求和公式：

$s_{2} = 5356 * ((1 - {0.2992905153099328}^{2}) / (1 - 0.2992905153099328))$

$s_{2} = 5356 * ((1 - 0.08957481255448511) / (1 - 0.2992905153099328))$

$s_{2} = 5356 * (0.9104251874455149 / (1 - 0.2992905153099328))$

$s_{2} = 5356 * (0.9104251874455149 / 0.7007094846900672)$

$s_{2} = 5356 \cdot 1.2992905153099328$

$s_{2} = 6959$

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： $a = 5, 356$ 和公比： $r = 0.2992905153099328$ 插入几何级数的公式：

$a_{n} = 5356 \cdot {0.2992905153099328}^{n - 1}$

4. 找到第n项

使用通用公式找到第n项

$a_{1} = 5356$

$a_{2} = a_{1} \cdot r^{n - 1} = 5356 \cdot {0.2992905153099328}^{2 - 1} = 5356 \cdot {0.2992905153099328}^{1} = 5356 \cdot 0.2992905153099328 = 1603$

$a_{3} = a_{1} \cdot r^{n - 1} = 5356 \cdot {0.2992905153099328}^{3 - 1} = 5356 \cdot {0.2992905153099328}^{2} = 5356 \cdot 0.08957481255448511 = 479.76269604182227$

$a_{4} = a_{1} \cdot r^{n - 1} = 5356 \cdot {0.2992905153099328}^{4 - 1} = 5356 \cdot {0.2992905153099328}^{3} = 5356 \cdot 0.026808891808222483 = 143.5884245248396$

$a_{5} = a_{1} \cdot r^{n - 1} = 5356 \cdot {0.2992905153099328}^{5 - 1} = 5356 \cdot {0.2992905153099328}^{4} = 5356 \cdot 0.008023647044171143 = 42.97465356858064$

$a_{6} = a_{1} \cdot r^{n - 1} = 5356 \cdot {0.2992905153099328}^{6 - 1} = 5356 \cdot {0.2992905153099328}^{5} = 5356 \cdot 0.0024014014585150003 = 12.861906211806343$

$a_{7} = a_{1} \cdot r^{n - 1} = 5356 \cdot {0.2992905153099328}^{7 - 1} = 5356 \cdot {0.2992905153099328}^{6} = 5356 \cdot 0.0007187166799849786 = 3.8494465379995453$

$a_{8} = a_{1} \cdot r^{n - 1} = 5356 \cdot {0.2992905153099328}^{8 - 1} = 5356 \cdot {0.2992905153099328}^{7} = 5356 \cdot 0.00021510508551454832 = 1.1521028380159208$

$a_{9} = a_{1} \cdot r^{n - 1} = 5356 \cdot {0.2992905153099328}^{9 - 1} = 5356 \cdot {0.2992905153099328}^{8} = 5356 \cdot 6.437891188943632 E - 05 = 0.3448134520798209$

$a_{10} = a_{1} \cdot r^{n - 1} = 5356 \cdot {0.2992905153099328}^{10 - 1} = 5356 \cdot {0.2992905153099328}^{9} = 5356 \cdot 1.9267997714482155 E - 05 = 0.10319939575876642$

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