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 = 0.011494252873563218

r=0.011494252873563218

该系列的和是：

s = 88

s=88

此系列的通用形式是：

a_{n} = 87 \cdot {0.011494252873563218}^{n - 1}

a_n=87*0.011494252873563218^(n-1)

这个序列的第n项是：

87, 1, 0.011494252873563218, 0.0001321178491214163, 1.518595966912831 E - 06, 1.745512605646932 E - 08, 2.006336328329807 E - 10, 2.306133710723916 E - 12, 2.6507284031309377 E - 14, 3.0468142564723423 E - 16

87,1,0.011494252873563218,0.0001321178491214163,1.518595966912831E-06,1.745512605646932E-08,2.006336328329807E-10,2.306133710723916E-12,2.6507284031309377E-14,3.0468142564723423E-16

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：

$a_{2} a_{1} = \frac{1}{87} = 0.011494252873563218$

该序列的公比（ $r$ ）保持不变，并且等于两个连续项的商。
$r = 0.011494252873563218$

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： $a = 87$ 、公比： $r = 0.011494252873563218$ 和元素数目 $n = 2$ 插入几何级数求和公式：

$s_{2} = 87 * ((1 - {0.011494252873563218}^{2}) / (1 - 0.011494252873563218))$

$s_{2} = 87 * ((1 - 0.0001321178491214163) / (1 - 0.011494252873563218))$

$s_{2} = 87 * (0.9998678821508786 / (1 - 0.011494252873563218))$

$s_{2} = 87 * (0.9998678821508786 / 0.9885057471264368)$

$s_{2} = 87 \cdot 1.0114942528735633$

$s_{2} = 88.00000000000001$

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： $a = 87$ 和公比： $r = 0.011494252873563218$ 插入几何级数的公式：

$a_{n} = 87 \cdot {0.011494252873563218}^{n - 1}$

4. 找到第n项

使用通用公式找到第n项

$a_{1} = 87$

$a_{2} = a_{1} \cdot r^{n - 1} = 87 \cdot {0.011494252873563218}^{2 - 1} = 87 \cdot {0.011494252873563218}^{1} = 87 \cdot 0.011494252873563218 = 1$

$a_{3} = a_{1} \cdot r^{n - 1} = 87 \cdot {0.011494252873563218}^{3 - 1} = 87 \cdot {0.011494252873563218}^{2} = 87 \cdot 0.0001321178491214163 = 0.011494252873563218$

$a_{4} = a_{1} \cdot r^{n - 1} = 87 \cdot {0.011494252873563218}^{4 - 1} = 87 \cdot {0.011494252873563218}^{3} = 87 \cdot 1.518595966912831 E - 06 = 0.0001321178491214163$

$a_{5} = a_{1} \cdot r^{n - 1} = 87 \cdot {0.011494252873563218}^{5 - 1} = 87 \cdot {0.011494252873563218}^{4} = 87 \cdot 1.745512605646932 E - 08 = 1.518595966912831 E - 06$

$a_{6} = a_{1} \cdot r^{n - 1} = 87 \cdot {0.011494252873563218}^{6 - 1} = 87 \cdot {0.011494252873563218}^{5} = 87 \cdot 2.006336328329807 E - 10 = 1.745512605646932 E - 08$

$a_{7} = a_{1} \cdot r^{n - 1} = 87 \cdot {0.011494252873563218}^{7 - 1} = 87 \cdot {0.011494252873563218}^{6} = 87 \cdot 2.306133710723916 E - 12 = 2.006336328329807 E - 10$

$a_{8} = a_{1} \cdot r^{n - 1} = 87 \cdot {0.011494252873563218}^{8 - 1} = 87 \cdot {0.011494252873563218}^{7} = 87 \cdot 2.650728403130938 E - 14 = 2.306133710723916 E - 12$

$a_{9} = a_{1} \cdot r^{n - 1} = 87 \cdot {0.011494252873563218}^{9 - 1} = 87 \cdot {0.011494252873563218}^{8} = 87 \cdot 3.0468142564723423 E - 16 = 2.6507284031309377 E - 14$

$a_{10} = a_{1} \cdot r^{n - 1} = 87 \cdot {0.011494252873563218}^{10 - 1} = 87 \cdot {0.011494252873563218}^{9} = 87 \cdot 3.50208535226706 E - 18 = 3.0468142564723423 E - 16$

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