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 = 0.5303030303030303

r=0.5303030303030303

该系列的和是：

s = 606000

s=606000

此系列的通用形式是：

a_{n} = 396000 \cdot {0.5303030303030303}^{n - 1}

a_n=396000*0.5303030303030303^(n-1)

这个序列的第n项是：

396000, 210000, 111363.63636363635, 59056.473829201095, 31317.82703063694, 16607.938576852925, 8807.240154391702, 4670.506142480447, 2476.783560406298, 1313.4458274881881

396000,210000,111363.63636363635,59056.473829201095,31317.82703063694,16607.938576852925,8807.240154391702,4670.506142480447,2476.783560406298,1313.4458274881881

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：

$a_{2} a_{1} = \frac{210000}{396000} = 0.5303030303030303$

该序列的公比（ $r$ ）保持不变，并且等于两个连续项的商。
$r = 0.5303030303030303$

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： $a = 396, 000$ 、公比： $r = 0.5303030303030303$ 和元素数目 $n = 2$ 插入几何级数求和公式：

$s_{2} = 396000 * ((1 - {0.5303030303030303}^{2}) / (1 - 0.5303030303030303))$

$s_{2} = 396000 * ((1 - 0.28122130394857664) / (1 - 0.5303030303030303))$

$s_{2} = 396000 * (0.7187786960514233 / (1 - 0.5303030303030303))$

$s_{2} = 396000 * (0.7187786960514233 / 0.4696969696969697)$

$s_{2} = 396000 \cdot 1.5303030303030303$

$s_{2} = 606000$

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： $a = 396, 000$ 和公比： $r = 0.5303030303030303$ 插入几何级数的公式：

$a_{n} = 396000 \cdot {0.5303030303030303}^{n - 1}$

4. 找到第n项

使用通用公式找到第n项

$a_{1} = 396000$

$a_{2} = a_{1} \cdot r^{n - 1} = 396000 \cdot {0.5303030303030303}^{2 - 1} = 396000 \cdot {0.5303030303030303}^{1} = 396000 \cdot 0.5303030303030303 = 210000$

$a_{3} = a_{1} \cdot r^{n - 1} = 396000 \cdot {0.5303030303030303}^{3 - 1} = 396000 \cdot {0.5303030303030303}^{2} = 396000 \cdot 0.28122130394857664 = 111363.63636363635$

$a_{4} = a_{1} \cdot r^{n - 1} = 396000 \cdot {0.5303030303030303}^{4 - 1} = 396000 \cdot {0.5303030303030303}^{3} = 396000 \cdot 0.14913250966969974 = 59056.473829201095$

$a_{5} = a_{1} \cdot r^{n - 1} = 396000 \cdot {0.5303030303030303}^{5 - 1} = 396000 \cdot {0.5303030303030303}^{4} = 396000 \cdot 0.07908542179453773 = 31317.82703063694$

$a_{6} = a_{1} \cdot r^{n - 1} = 396000 \cdot {0.5303030303030303}^{6 - 1} = 396000 \cdot {0.5303030303030303}^{5} = 396000 \cdot 0.041939238830436674 = 16607.938576852925$

$a_{7} = a_{1} \cdot r^{n - 1} = 396000 \cdot {0.5303030303030303}^{7 - 1} = 396000 \cdot {0.5303030303030303}^{6} = 396000 \cdot 0.022240505440383085 = 8807.240154391702$

$a_{8} = a_{1} \cdot r^{n - 1} = 396000 \cdot {0.5303030303030303}^{8 - 1} = 396000 \cdot {0.5303030303030303}^{7} = 396000 \cdot 0.01179420743050618 = 4670.506142480447$

$a_{9} = a_{1} \cdot r^{n - 1} = 396000 \cdot {0.5303030303030303}^{9 - 1} = 396000 \cdot {0.5303030303030303}^{8} = 396000 \cdot 0.006254503940419944 = 2476.783560406298$

$a_{10} = a_{1} \cdot r^{n - 1} = 396000 \cdot {0.5303030303030303}^{10 - 1} = 396000 \cdot {0.5303030303030303}^{9} = 396000 \cdot 0.0033167823926469396 = 1313.4458274881881$

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