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 = 0.039603960396039604

r=0.039603960396039604

该系列的和是：

s = 105

s=105

此系列的通用形式是：

a_{n} = 101 \cdot {0.039603960396039604}^{n - 1}

a_n=101*0.039603960396039604^(n-1)

这个序列的第n项是：

101, 4, 0.15841584158415842, 0.006273894716204294, 0.000248471077869477, 9.840438727504039 E - 06, 3.897203456437243 E - 07, 1.5434469134404923 E - 08, 6.112661043328683 E - 10, 2.420855858744033 E - 11

101,4,0.15841584158415842,0.006273894716204294,0.000248471077869477,9.840438727504039E-06,3.897203456437243E-07,1.5434469134404923E-08,6.112661043328683E-10,2.420855858744033E-11

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：

$a_{2} a_{1} = \frac{4}{101} = 0.039603960396039604$

该序列的公比（ $r$ ）保持不变，并且等于两个连续项的商。
$r = 0.039603960396039604$

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： $a = 101$ 、公比： $r = 0.039603960396039604$ 和元素数目 $n = 2$ 插入几何级数求和公式：

$s_{2} = 101 * ((1 - {0.039603960396039604}^{2}) / (1 - 0.039603960396039604))$

$s_{2} = 101 * ((1 - 0.0015684736790510735) / (1 - 0.039603960396039604))$

$s_{2} = 101 * (0.9984315263209489 / (1 - 0.039603960396039604))$

$s_{2} = 101 * (0.9984315263209489 / 0.9603960396039604)$

$s_{2} = 101 \cdot 1.0396039603960396$

$s_{2} = 105$

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： $a = 101$ 和公比： $r = 0.039603960396039604$ 插入几何级数的公式：

$a_{n} = 101 \cdot {0.039603960396039604}^{n - 1}$

4. 找到第n项

使用通用公式找到第n项

$a_{1} = 101$

$a_{2} = a_{1} \cdot r^{n - 1} = 101 \cdot {0.039603960396039604}^{2 - 1} = 101 \cdot {0.039603960396039604}^{1} = 101 \cdot 0.039603960396039604 = 4$

$a_{3} = a_{1} \cdot r^{n - 1} = 101 \cdot {0.039603960396039604}^{3 - 1} = 101 \cdot {0.039603960396039604}^{2} = 101 \cdot 0.0015684736790510735 = 0.15841584158415842$

$a_{4} = a_{1} \cdot r^{n - 1} = 101 \cdot {0.039603960396039604}^{4 - 1} = 101 \cdot {0.039603960396039604}^{3} = 101 \cdot 6.211776946736924 E - 05 = 0.006273894716204294$

$a_{5} = a_{1} \cdot r^{n - 1} = 101 \cdot {0.039603960396039604}^{5 - 1} = 101 \cdot {0.039603960396039604}^{4} = 101 \cdot 2.4601096818760098 E - 06 = 0.000248471077869477$

$a_{6} = a_{1} \cdot r^{n - 1} = 101 \cdot {0.039603960396039604}^{6 - 1} = 101 \cdot {0.039603960396039604}^{5} = 101 \cdot 9.743008641093109 E - 08 = 9.840438727504039 E - 06$

$a_{7} = a_{1} \cdot r^{n - 1} = 101 \cdot {0.039603960396039604}^{7 - 1} = 101 \cdot {0.039603960396039604}^{6} = 101 \cdot 3.858617283601231 E - 09 = 3.897203456437243 E - 07$

$a_{8} = a_{1} \cdot r^{n - 1} = 101 \cdot {0.039603960396039604}^{8 - 1} = 101 \cdot {0.039603960396039604}^{7} = 101 \cdot 1.5281652608321708 E - 10 = 1.5434469134404923 E - 08$

$a_{9} = a_{1} \cdot r^{n - 1} = 101 \cdot {0.039603960396039604}^{9 - 1} = 101 \cdot {0.039603960396039604}^{8} = 101 \cdot 6.0521396468600825 E - 12 = 6.112661043328683 E - 10$

$a_{10} = a_{1} \cdot r^{n - 1} = 101 \cdot {0.039603960396039604}^{10 - 1} = 101 \cdot {0.039603960396039604}^{9} = 101 \cdot 2.396886988855478 E - 13 = 2.420855858744033 E - 11$

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