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 = 7.410493827160494

r=7.410493827160494

该系列的和是：

s = 8240400

s=8240400

此系列的通用形式是：

a_{n} = 979776 \cdot {7.410493827160494}^{n - 1}

a_n=979776*7.410493827160494^(n-1)

这个序列的第n项是：

979776, 7260624, 53804809.33333333, 398720207.43621397, 2954713635.9702153, 21895887160.384216, 162259336642.22995, 1202421812586.4014, 8910539419814.66, 66031497367206.78

979776,7260624,53804809.33333333,398720207.43621397,2954713635.9702153,21895887160.384216,162259336642.22995,1202421812586.4014,8910539419814.66,66031497367206.78

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：

$a_{2} a_{1} = \frac{7260624}{979776} = 7.410493827160494$

该序列的公比（ $r$ ）保持不变，并且等于两个连续项的商。
$r = 7.410493827160494$

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： $a = 979, 776$ 、公比： $r = 7.410493827160494$ 和元素数目 $n = 2$ 插入几何级数求和公式：

$s_{2} = 979776 * ((1 - {7.410493827160494}^{2}) / (1 - 7.410493827160494))$

$s_{2} = 979776 * ((1 - 54.91541876238378) / (1 - 7.410493827160494))$

$s_{2} = 979776 * (- 53.91541876238378 / (1 - 7.410493827160494))$

$s_{2} = 979776 * (- 53.91541876238378 / - 6.410493827160494)$

$s_{2} = 979776 \cdot 8.410493827160494$

$s_{2} = 8240400$

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： $a = 979, 776$ 和公比： $r = 7.410493827160494$ 插入几何级数的公式：

$a_{n} = 979776 \cdot {7.410493827160494}^{n - 1}$

4. 找到第n项

使用通用公式找到第n项

$a_{1} = 979776$

$a_{2} = a_{1} \cdot r^{n - 1} = 979776 \cdot {7.410493827160494}^{2 - 1} = 979776 \cdot {7.410493827160494}^{1} = 979776 \cdot 7.410493827160494 = 7260624$

$a_{3} = a_{1} \cdot r^{n - 1} = 979776 \cdot {7.410493827160494}^{3 - 1} = 979776 \cdot {7.410493827160494}^{2} = 979776 \cdot 54.91541876238378 = 53804809.33333333$

$a_{4} = a_{1} \cdot r^{n - 1} = 979776 \cdot {7.410493827160494}^{4 - 1} = 979776 \cdot {7.410493827160494}^{3} = 979776 \cdot 406.95037175457855 = 398720207.43621397$

$a_{5} = a_{1} \cdot r^{n - 1} = 979776 \cdot {7.410493827160494}^{5 - 1} = 979776 \cdot {7.410493827160494}^{4} = 979776 \cdot 3015.7032178479726 = 2954713635.9702153$

$a_{6} = a_{1} \cdot r^{n - 1} = 979776 \cdot {7.410493827160494}^{6 - 1} = 979776 \cdot {7.410493827160494}^{5} = 979776 \cdot 22347.850080410437 = 21895887160.384216$

$a_{7} = a_{1} \cdot r^{n - 1} = 979776 \cdot {7.410493827160494}^{7 - 1} = 979776 \cdot {7.410493827160494}^{6} = 979776 \cdot 165608.6050711897 = 162259336642.22995$

$a_{8} = a_{1} \cdot r^{n - 1} = 979776 \cdot {7.410493827160494}^{8 - 1} = 979776 \cdot {7.410493827160494}^{7} = 979776 \cdot 1227241.5456047112 = 1202421812586.4014$

$a_{9} = a_{1} \cdot r^{n - 1} = 979776 \cdot {7.410493827160494}^{9 - 1} = 979776 \cdot {7.410493827160494}^{8} = 979776 \cdot 9094465.898138616 = 8910539419814.66$

$a_{10} = a_{1} \cdot r^{n - 1} = 979776 \cdot {7.410493827160494}^{10 - 1} = 979776 \cdot {7.410493827160494}^{9} = 979776 \cdot 67394483.39947782 = 66031497367206.78$

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