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 = 0.631578947368421

r=0.631578947368421

该系列的和是：

s = 124

s=124

此系列的通用形式是：

a_{n} = 76 \cdot {0.631578947368421}^{n - 1}

a_n=76*0.631578947368421^(n-1)

这个序列的第n项是：

76, 48, 30.31578947368421, 19.14681440443213, 12.092724887009766, 7.637510454953535, 4.823690813654864, 3.0465415665188615, 1.924131515696123, 1.2152409572817617

76,48,30.31578947368421,19.14681440443213,12.092724887009766,7.637510454953535,4.823690813654864,3.0465415665188615,1.924131515696123,1.2152409572817617

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：

$a_{2} a_{1} = \frac{48}{76} = 0.631578947368421$

该序列的公比（ $r$ ）保持不变，并且等于两个连续项的商。
$r = 0.631578947368421$

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： $a = 76$ 、公比： $r = 0.631578947368421$ 和元素数目 $n = 2$ 插入几何级数求和公式：

$s_{2} = 76 * ((1 - {0.631578947368421}^{2}) / (1 - 0.631578947368421))$

$s_{2} = 76 * ((1 - 0.39889196675900274) / (1 - 0.631578947368421))$

$s_{2} = 76 * (0.6011080332409973 / (1 - 0.631578947368421))$

$s_{2} = 76 * (0.6011080332409973 / 0.368421052631579)$

$s_{2} = 76 \cdot 1.631578947368421$

$s_{2} = 124$

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： $a = 76$ 和公比： $r = 0.631578947368421$ 插入几何级数的公式：

$a_{n} = 76 \cdot {0.631578947368421}^{n - 1}$

4. 找到第n项

使用通用公式找到第n项

$a_{1} = 76$

$a_{2} = a_{1} \cdot r^{n - 1} = 76 \cdot {0.631578947368421}^{2 - 1} = 76 \cdot {0.631578947368421}^{1} = 76 \cdot 0.631578947368421 = 48$

$a_{3} = a_{1} \cdot r^{n - 1} = 76 \cdot {0.631578947368421}^{3 - 1} = 76 \cdot {0.631578947368421}^{2} = 76 \cdot 0.39889196675900274 = 30.31578947368421$

$a_{4} = a_{1} \cdot r^{n - 1} = 76 \cdot {0.631578947368421}^{4 - 1} = 76 \cdot {0.631578947368421}^{3} = 76 \cdot 0.25193176847937016 = 19.14681440443213$

$a_{5} = a_{1} \cdot r^{n - 1} = 76 \cdot {0.631578947368421}^{5 - 1} = 76 \cdot {0.631578947368421}^{4} = 76 \cdot 0.15911480114486534 = 12.092724887009766$

$a_{6} = a_{1} \cdot r^{n - 1} = 76 \cdot {0.631578947368421}^{6 - 1} = 76 \cdot {0.631578947368421}^{5} = 76 \cdot 0.10049355861780968 = 7.637510454953535$

$a_{7} = a_{1} \cdot r^{n - 1} = 76 \cdot {0.631578947368421}^{7 - 1} = 76 \cdot {0.631578947368421}^{6} = 76 \cdot 0.06346961596914295 = 4.823690813654864$

$a_{8} = a_{1} \cdot r^{n - 1} = 76 \cdot {0.631578947368421}^{8 - 1} = 76 \cdot {0.631578947368421}^{7} = 76 \cdot 0.04008607324366923 = 3.0465415665188615$

$a_{9} = a_{1} \cdot r^{n - 1} = 76 \cdot {0.631578947368421}^{9 - 1} = 76 \cdot {0.631578947368421}^{8} = 76 \cdot 0.02531751994337004 = 1.924131515696123$

$a_{10} = a_{1} \cdot r^{n - 1} = 76 \cdot {0.631578947368421}^{10 - 1} = 76 \cdot {0.631578947368421}^{9} = 76 \cdot 0.015990012595812654 = 1.2152409572817617$

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