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 = 1.3636363636363635

r=1.3636363636363635

该系列的和是：

s = 26

s=26

此系列的通用形式是：

a_{n} = 11 \cdot {1.3636363636363635}^{n - 1}

a_n=11*1.3636363636363635^(n-1)

这个序列的第n项是：

11, 14.999999999999998, 20.454545454545453, 27.89256198347107, 38.035311795642365, 51.86633426678504, 70.72681945470686, 96.44566289278207, 131.51681303561193, 179.3411086849253

11,14.999999999999998,20.454545454545453,27.89256198347107,38.035311795642365,51.86633426678504,70.72681945470686,96.44566289278207,131.51681303561193,179.3411086849253

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：

$a_{2} a_{1} = \frac{15}{11} = 1.3636363636363635$

该序列的公比（ $r$ ）保持不变，并且等于两个连续项的商。
$r = 1.3636363636363635$

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： $a = 11$ 、公比： $r = 1.3636363636363635$ 和元素数目 $n = 2$ 插入几何级数求和公式：

$s_{2} = 11 * ((1 - {1.3636363636363635}^{2}) / (1 - 1.3636363636363635))$

$s_{2} = 11 * ((1 - 1.8595041322314048) / (1 - 1.3636363636363635))$

$s_{2} = 11 * (- 0.8595041322314048 / (1 - 1.3636363636363635))$

$s_{2} = 11 * (- 0.8595041322314048 / - 0.36363636363636354)$

$s_{2} = 11 \cdot 2.3636363636363638$

$s_{2} = 26$

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： $a = 11$ 和公比： $r = 1.3636363636363635$ 插入几何级数的公式：

$a_{n} = 11 \cdot {1.3636363636363635}^{n - 1}$

4. 找到第n项

使用通用公式找到第n项

$a_{1} = 11$

$a_{2} = a_{1} \cdot r^{n - 1} = 11 \cdot {1.3636363636363635}^{2 - 1} = 11 \cdot {1.3636363636363635}^{1} = 11 \cdot 1.3636363636363635 = 14.999999999999998$

$a_{3} = a_{1} \cdot r^{n - 1} = 11 \cdot {1.3636363636363635}^{3 - 1} = 11 \cdot {1.3636363636363635}^{2} = 11 \cdot 1.8595041322314048 = 20.454545454545453$

$a_{4} = a_{1} \cdot r^{n - 1} = 11 \cdot {1.3636363636363635}^{4 - 1} = 11 \cdot {1.3636363636363635}^{3} = 11 \cdot 2.5356874530428244 = 27.89256198347107$

$a_{5} = a_{1} \cdot r^{n - 1} = 11 \cdot {1.3636363636363635}^{5 - 1} = 11 \cdot {1.3636363636363635}^{4} = 11 \cdot 3.4577556177856694 = 38.035311795642365$

$a_{6} = a_{1} \cdot r^{n - 1} = 11 \cdot {1.3636363636363635}^{6 - 1} = 11 \cdot {1.3636363636363635}^{5} = 11 \cdot 4.715121296980458 = 51.86633426678504$

$a_{7} = a_{1} \cdot r^{n - 1} = 11 \cdot {1.3636363636363635}^{7 - 1} = 11 \cdot {1.3636363636363635}^{6} = 11 \cdot 6.4297108595188055 = 70.72681945470686$

$a_{8} = a_{1} \cdot r^{n - 1} = 11 \cdot {1.3636363636363635}^{8 - 1} = 11 \cdot {1.3636363636363635}^{7} = 11 \cdot 8.76778753570746 = 96.44566289278207$

$a_{9} = a_{1} \cdot r^{n - 1} = 11 \cdot {1.3636363636363635}^{9 - 1} = 11 \cdot {1.3636363636363635}^{8} = 11 \cdot 11.956073912328357 = 131.51681303561193$

$a_{10} = a_{1} \cdot r^{n - 1} = 11 \cdot {1.3636363636363635}^{10 - 1} = 11 \cdot {1.3636363636363635}^{9} = 11 \cdot 16.303737153175028 = 179.3411086849253$

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