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 = 0.18421052631578946

r=0.18421052631578946

该系列的和是：

s = 45

s=45

此系列的通用形式是：

a_{n} = 38 \cdot {0.18421052631578946}^{n - 1}

a_n=38*0.18421052631578946^(n-1)

这个序列的第n项是：

38, 7, 1.289473684210526, 0.23753462603878112, 0.0437563784808281, 0.008060385509626228, 0.0014848078570364105, 0.00027351723682249665, 5.038475415151254 E - 05, 9.281402080541782 E - 06

38,7,1.289473684210526,0.23753462603878112,0.0437563784808281,0.008060385509626228,0.0014848078570364105,0.00027351723682249665,5.038475415151254E-05,9.281402080541782E-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：

$a_{2} a_{1} = \frac{7}{38} = 0.18421052631578946$

该序列的公比（ $r$ ）保持不变，并且等于两个连续项的商。
$r = 0.18421052631578946$

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： $a = 38$ 、公比： $r = 0.18421052631578946$ 和元素数目 $n = 2$ 插入几何级数求和公式：

$s_{2} = 38 * ((1 - {0.18421052631578946}^{2}) / (1 - 0.18421052631578946))$

$s_{2} = 38 * ((1 - 0.03393351800554016) / (1 - 0.18421052631578946))$

$s_{2} = 38 * (0.9660664819944599 / (1 - 0.18421052631578946))$

$s_{2} = 38 * (0.9660664819944599 / 0.8157894736842105)$

$s_{2} = 38 \cdot 1.1842105263157896$

$s_{2} = 45.00000000000001$

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： $a = 38$ 和公比： $r = 0.18421052631578946$ 插入几何级数的公式：

$a_{n} = 38 \cdot {0.18421052631578946}^{n - 1}$

4. 找到第n项

使用通用公式找到第n项

$a_{1} = 38$

$a_{2} = a_{1} \cdot r^{n - 1} = 38 \cdot {0.18421052631578946}^{2 - 1} = 38 \cdot {0.18421052631578946}^{1} = 38 \cdot 0.18421052631578946 = 7$

$a_{3} = a_{1} \cdot r^{n - 1} = 38 \cdot {0.18421052631578946}^{3 - 1} = 38 \cdot {0.18421052631578946}^{2} = 38 \cdot 0.03393351800554016 = 1.289473684210526$

$a_{4} = a_{1} \cdot r^{n - 1} = 38 \cdot {0.18421052631578946}^{4 - 1} = 38 \cdot {0.18421052631578946}^{3} = 38 \cdot 0.006250911211546872 = 0.23753462603878112$

$a_{5} = a_{1} \cdot r^{n - 1} = 38 \cdot {0.18421052631578946}^{5 - 1} = 38 \cdot {0.18421052631578946}^{4} = 38 \cdot 0.0011514836442323183 = 0.0437563784808281$

$a_{6} = a_{1} \cdot r^{n - 1} = 38 \cdot {0.18421052631578946}^{6 - 1} = 38 \cdot {0.18421052631578946}^{5} = 38 \cdot 0.00021211540814805864 = 0.008060385509626228$

$a_{7} = a_{1} \cdot r^{n - 1} = 38 \cdot {0.18421052631578946}^{7 - 1} = 38 \cdot {0.18421052631578946}^{6} = 38 \cdot 3.907389097464238 E - 05 = 0.0014848078570364105$

$a_{8} = a_{1} \cdot r^{n - 1} = 38 \cdot {0.18421052631578946}^{8 - 1} = 38 \cdot {0.18421052631578946}^{7} = 38 \cdot 7.197822021644648 E - 06 = 0.00027351723682249665$

$a_{9} = a_{1} \cdot r^{n - 1} = 38 \cdot {0.18421052631578946}^{9 - 1} = 38 \cdot {0.18421052631578946}^{8} = 38 \cdot 1.3259145829345404 E - 06 = 5.038475415151254 E - 05$

$a_{10} = a_{1} \cdot r^{n - 1} = 38 \cdot {0.18421052631578946}^{10 - 1} = 38 \cdot {0.18421052631578946}^{9} = 38 \cdot 2.4424742317215214 E - 07 = 9.281402080541782 E - 06$

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