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 = 0.005291005291005291

r=0.005291005291005291

该系列的和是：

s = 380

s=380

此系列的通用形式是：

a_{n} = 378 \cdot {0.005291005291005291}^{n - 1}

a_n=378*0.005291005291005291^(n-1)

这个序列的第n项是：

378, 2, 0.010582010582010581, 5.5989473978891965 E - 05, 2.9624060306292044 E - 07, 1.5674105982165101 E - 09, 8.293177768341323 E - 12, 4.3879247451541383 E - 14, 2.321653304314359 E - 16, 1.228387991700719 E - 18

378,2,0.010582010582010581,5.5989473978891965E-05,2.9624060306292044E-07,1.5674105982165101E-09,8.293177768341323E-12,4.3879247451541383E-14,2.321653304314359E-16,1.228387991700719E-18

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：

$a_{2} a_{1} = \frac{2}{378} = 0.005291005291005291$

该序列的公比（ $r$ ）保持不变，并且等于两个连续项的商。
$r = 0.005291005291005291$

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： $a = 378$ 、公比： $r = 0.005291005291005291$ 和元素数目 $n = 2$ 插入几何级数求和公式：

$s_{2} = 378 * ((1 - {0.005291005291005291}^{2}) / (1 - 0.005291005291005291))$

$s_{2} = 378 * ((1 - 2.7994736989445982 E - 05) / (1 - 0.005291005291005291))$

$s_{2} = 378 * (0.9999720052630106 / (1 - 0.005291005291005291))$

$s_{2} = 378 * (0.9999720052630106 / 0.9947089947089947)$

$s_{2} = 378 \cdot 1.0052910052910053$

$s_{2} = 380$

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： $a = 378$ 和公比： $r = 0.005291005291005291$ 插入几何级数的公式：

$a_{n} = 378 \cdot {0.005291005291005291}^{n - 1}$

4. 找到第n项

使用通用公式找到第n项

$a_{1} = 378$

$a_{2} = a_{1} \cdot r^{n - 1} = 378 \cdot {0.005291005291005291}^{2 - 1} = 378 \cdot {0.005291005291005291}^{1} = 378 \cdot 0.005291005291005291 = 2$

$a_{3} = a_{1} \cdot r^{n - 1} = 378 \cdot {0.005291005291005291}^{3 - 1} = 378 \cdot {0.005291005291005291}^{2} = 378 \cdot 2.7994736989445982 E - 05 = 0.010582010582010581$

$a_{4} = a_{1} \cdot r^{n - 1} = 378 \cdot {0.005291005291005291}^{4 - 1} = 378 \cdot {0.005291005291005291}^{3} = 378 \cdot 1.4812030153146022 E - 07 = 5.5989473978891965 E - 05$

$a_{5} = a_{1} \cdot r^{n - 1} = 378 \cdot {0.005291005291005291}^{5 - 1} = 378 \cdot {0.005291005291005291}^{4} = 378 \cdot 7.837052991082551 E - 10 = 2.9624060306292044 E - 07$

$a_{6} = a_{1} \cdot r^{n - 1} = 378 \cdot {0.005291005291005291}^{6 - 1} = 378 \cdot {0.005291005291005291}^{5} = 378 \cdot 4.146588884170662 E - 12 = 1.5674105982165101 E - 09$

$a_{7} = a_{1} \cdot r^{n - 1} = 378 \cdot {0.005291005291005291}^{7 - 1} = 378 \cdot {0.005291005291005291}^{6} = 378 \cdot 2.1939623725770695 E - 14 = 8.293177768341323 E - 12$

$a_{8} = a_{1} \cdot r^{n - 1} = 378 \cdot {0.005291005291005291}^{8 - 1} = 378 \cdot {0.005291005291005291}^{7} = 378 \cdot 1.1608266521571795 E - 16 = 4.3879247451541383 E - 14$

$a_{9} = a_{1} \cdot r^{n - 1} = 378 \cdot {0.005291005291005291}^{9 - 1} = 378 \cdot {0.005291005291005291}^{8} = 378 \cdot 6.141939958503595 E - 19 = 2.321653304314359 E - 16$

$a_{10} = a_{1} \cdot r^{n - 1} = 378 \cdot {0.005291005291005291}^{10 - 1} = 378 \cdot {0.005291005291005291}^{9} = 378 \cdot 3.2497036817479337 E - 21 = 1.228387991700719 E - 18$

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