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 = 0.05785123966942149

r=0.05785123966942149

该系列的和是：

s = 9856

s=9856

此系列的通用形式是：

a_{n} = 9317 \cdot {0.05785123966942149}^{n - 1}

a_n=9317*0.05785123966942149^(n-1)

这个序列的第n项是：

9317, 539, 31.181818181818183, 1.8039068369646885, 0.10435824676655221, 0.006037253945172443, 0.0003492626249273314, 2.0205275822242315 E - 05, 1.1689002541793074 E - 06, 6.762232875417481 E - 08

9317,539,31.181818181818183,1.8039068369646885,0.10435824676655221,0.006037253945172443,0.0003492626249273314,2.0205275822242315E-05,1.1689002541793074E-06,6.762232875417481E-08

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：

$a_{2} a_{1} = \frac{539}{9317} = 0.05785123966942149$

该序列的公比（ $r$ ）保持不变，并且等于两个连续项的商。
$r = 0.05785123966942149$

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： $a = 9, 317$ 、公比： $r = 0.05785123966942149$ 和元素数目 $n = 2$ 插入几何级数求和公式：

$s_{2} = 9317 * ((1 - {0.05785123966942149}^{2}) / (1 - 0.05785123966942149))$

$s_{2} = 9317 * ((1 - 0.0033467659312888466) / (1 - 0.05785123966942149))$

$s_{2} = 9317 * (0.9966532340687112 / (1 - 0.05785123966942149))$

$s_{2} = 9317 * (0.9966532340687112 / 0.9421487603305785)$

$s_{2} = 9317 \cdot 1.0578512396694215$

$s_{2} = 9856$

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： $a = 9, 317$ 和公比： $r = 0.05785123966942149$ 插入几何级数的公式：

$a_{n} = 9317 \cdot {0.05785123966942149}^{n - 1}$

4. 找到第n项

使用通用公式找到第n项

$a_{1} = 9317$

$a_{2} = a_{1} \cdot r^{n - 1} = 9317 \cdot {0.05785123966942149}^{2 - 1} = 9317 \cdot {0.05785123966942149}^{1} = 9317 \cdot 0.05785123966942149 = 539$

$a_{3} = a_{1} \cdot r^{n - 1} = 9317 \cdot {0.05785123966942149}^{3 - 1} = 9317 \cdot {0.05785123966942149}^{2} = 9317 \cdot 0.0033467659312888466 = 31.181818181818183$

$a_{4} = a_{1} \cdot r^{n - 1} = 9317 \cdot {0.05785123966942149}^{4 - 1} = 9317 \cdot {0.05785123966942149}^{3} = 9317 \cdot 0.00019361455800844568 = 1.8039068369646885$

$a_{5} = a_{1} \cdot r^{n - 1} = 9317 \cdot {0.05785123966942149}^{5 - 1} = 9317 \cdot {0.05785123966942149}^{4} = 9317 \cdot 1.12008421988357 E - 05 = 0.10435824676655221$

$a_{6} = a_{1} \cdot r^{n - 1} = 9317 \cdot {0.05785123966942149}^{6 - 1} = 9317 \cdot {0.05785123966942149}^{5} = 9317 \cdot 6.479826065442141 E - 07 = 0.006037253945172443$

$a_{7} = a_{1} \cdot r^{n - 1} = 9317 \cdot {0.05785123966942149}^{7 - 1} = 9317 \cdot {0.05785123966942149}^{6} = 9317 \cdot 3.7486597072805775 E - 08 = 0.0003492626249273314$

$a_{8} = a_{1} \cdot r^{n - 1} = 9317 \cdot {0.05785123966942149}^{8 - 1} = 9317 \cdot {0.05785123966942149}^{7} = 9317 \cdot 2.168646111649921 E - 09 = 2.0205275822242315 E - 05$

$a_{9} = a_{1} \cdot r^{n - 1} = 9317 \cdot {0.05785123966942149}^{9 - 1} = 9317 \cdot {0.05785123966942149}^{8} = 9317 \cdot 1.2545886596321856 E - 10 = 1.1689002541793074 E - 06$

$a_{10} = a_{1} \cdot r^{n - 1} = 9317 \cdot {0.05785123966942149}^{10 - 1} = 9317 \cdot {0.05785123966942149}^{9} = 9317 \cdot 7.2579509234919834 E - 12 = 6.762232875417481 E - 08$

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