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 = 0.14772727272727273

r=0.14772727272727273

该系列的和是：

s = 101

s=101

此系列的通用形式是：

a_{n} = 88 \cdot {0.14772727272727273}^{n - 1}

a_n=88*0.14772727272727273^(n-1)

这个序列的第n项是：

88, 13, 1.9204545454545459, 0.2837035123966943, 0.04191074614951166, 0.006191360226632405, 0.0009146327607525143, 0.00013511620329298505, 1.9960348213736432 E - 05, 2.9486878043019732 E - 06

88,13,1.9204545454545459,0.2837035123966943,0.04191074614951166,0.006191360226632405,0.0009146327607525143,0.00013511620329298505,1.9960348213736432E-05,2.9486878043019732E-06

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：

$a_{2} a_{1} = \frac{13}{88} = 0.14772727272727273$

该序列的公比（ $r$ ）保持不变，并且等于两个连续项的商。
$r = 0.14772727272727273$

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： $a = 88$ 、公比： $r = 0.14772727272727273$ 和元素数目 $n = 2$ 插入几何级数求和公式：

$s_{2} = 88 * ((1 - {0.14772727272727273}^{2}) / (1 - 0.14772727272727273))$

$s_{2} = 88 * ((1 - 0.02182334710743802) / (1 - 0.14772727272727273))$

$s_{2} = 88 * (0.978176652892562 / (1 - 0.14772727272727273))$

$s_{2} = 88 * (0.978176652892562 / 0.8522727272727273)$

$s_{2} = 88 \cdot 1.1477272727272727$

$s_{2} = 101$

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： $a = 88$ 和公比： $r = 0.14772727272727273$ 插入几何级数的公式：

$a_{n} = 88 \cdot {0.14772727272727273}^{n - 1}$

4. 找到第n项

使用通用公式找到第n项

$a_{1} = 88$

$a_{2} = a_{1} \cdot r^{n - 1} = 88 \cdot {0.14772727272727273}^{2 - 1} = 88 \cdot {0.14772727272727273}^{1} = 88 \cdot 0.14772727272727273 = 13$

$a_{3} = a_{1} \cdot r^{n - 1} = 88 \cdot {0.14772727272727273}^{3 - 1} = 88 \cdot {0.14772727272727273}^{2} = 88 \cdot 0.02182334710743802 = 1.9204545454545459$

$a_{4} = a_{1} \cdot r^{n - 1} = 88 \cdot {0.14772727272727273}^{4 - 1} = 88 \cdot {0.14772727272727273}^{3} = 88 \cdot 0.0032239035499624347 = 0.2837035123966943$

$a_{5} = a_{1} \cdot r^{n - 1} = 88 \cdot {0.14772727272727273}^{5 - 1} = 88 \cdot {0.14772727272727273}^{4} = 88 \cdot 0.00047625847897172336 = 0.04191074614951166$

$a_{6} = a_{1} \cdot r^{n - 1} = 88 \cdot {0.14772727272727273}^{6 - 1} = 88 \cdot {0.14772727272727273}^{5} = 88 \cdot 7.035636621173187 E - 05 = 0.006191360226632405$

$a_{7} = a_{1} \cdot r^{n - 1} = 88 \cdot {0.14772727272727273}^{7 - 1} = 88 \cdot {0.14772727272727273}^{6} = 88 \cdot 1.039355409946039 E - 05 = 0.0009146327607525143$

$a_{8} = a_{1} \cdot r^{n - 1} = 88 \cdot {0.14772727272727273}^{8 - 1} = 88 \cdot {0.14772727272727273}^{7} = 88 \cdot 1.5354114010566484 E - 06 = 0.00013511620329298505$

$a_{9} = a_{1} \cdot r^{n - 1} = 88 \cdot {0.14772727272727273}^{9 - 1} = 88 \cdot {0.14772727272727273}^{8} = 88 \cdot 2.2682213879245945 E - 07 = 1.9960348213736432 E - 05$

$a_{10} = a_{1} \cdot r^{n - 1} = 88 \cdot {0.14772727272727273}^{10 - 1} = 88 \cdot {0.14772727272727273}^{9} = 88 \cdot 3.350781595797697 E - 08 = 2.9486878043019732 E - 06$

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