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 = 0.2459016393442623

r=0.2459016393442623

该系列的和是：

s = 76

s=76

此系列的通用形式是：

a_{n} = 61 \cdot {0.2459016393442623}^{n - 1}

a_n=61*0.2459016393442623^(n-1)

这个序列的第n项是：

61, 15, 3.6885245901639343, 0.9070142434829347, 0.2230362893810495, 0.05484498919206135, 0.013486472752146234, 0.003316345758724484, 0.0008154948587027419, 0.00020053152263182177

61,15,3.6885245901639343,0.9070142434829347,0.2230362893810495,0.05484498919206135,0.013486472752146234,0.003316345758724484,0.0008154948587027419,0.00020053152263182177

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：

$a_{2} a_{1} = \frac{15}{61} = 0.2459016393442623$

该序列的公比（ $r$ ）保持不变，并且等于两个连续项的商。
$r = 0.2459016393442623$

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： $a = 61$ 、公比： $r = 0.2459016393442623$ 和元素数目 $n = 2$ 插入几何级数求和公式：

$s_{2} = 61 * ((1 - {0.2459016393442623}^{2}) / (1 - 0.2459016393442623))$

$s_{2} = 61 * ((1 - 0.060467616232195646) / (1 - 0.2459016393442623))$

$s_{2} = 61 * (0.9395323837678043 / (1 - 0.2459016393442623))$

$s_{2} = 61 * (0.9395323837678043 / 0.7540983606557377)$

$s_{2} = 61 \cdot 1.2459016393442623$

$s_{2} = 76$

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： $a = 61$ 和公比： $r = 0.2459016393442623$ 插入几何级数的公式：

$a_{n} = 61 \cdot {0.2459016393442623}^{n - 1}$

4. 找到第n项

使用通用公式找到第n项

$a_{1} = 61$

$a_{2} = a_{1} \cdot r^{n - 1} = 61 \cdot {0.2459016393442623}^{2 - 1} = 61 \cdot {0.2459016393442623}^{1} = 61 \cdot 0.2459016393442623 = 15$

$a_{3} = a_{1} \cdot r^{n - 1} = 61 \cdot {0.2459016393442623}^{3 - 1} = 61 \cdot {0.2459016393442623}^{2} = 61 \cdot 0.060467616232195646 = 3.6885245901639343$

$a_{4} = a_{1} \cdot r^{n - 1} = 61 \cdot {0.2459016393442623}^{4 - 1} = 61 \cdot {0.2459016393442623}^{3} = 61 \cdot 0.014869085958736634 = 0.9070142434829347$

$a_{5} = a_{1} \cdot r^{n - 1} = 61 \cdot {0.2459016393442623}^{5 - 1} = 61 \cdot {0.2459016393442623}^{4} = 61 \cdot 0.00365633261280409 = 0.2230362893810495$

$a_{6} = a_{1} \cdot r^{n - 1} = 61 \cdot {0.2459016393442623}^{6 - 1} = 61 \cdot {0.2459016393442623}^{5} = 61 \cdot 0.0008990981834764156 = 0.05484498919206135$

$a_{7} = a_{1} \cdot r^{n - 1} = 61 \cdot {0.2459016393442623}^{7 - 1} = 61 \cdot {0.2459016393442623}^{6} = 61 \cdot 0.00022108971724829892 = 0.013486472752146234$

$a_{8} = a_{1} \cdot r^{n - 1} = 61 \cdot {0.2459016393442623}^{8 - 1} = 61 \cdot {0.2459016393442623}^{7} = 61 \cdot 5.436632391351613 E - 05 = 0.003316345758724484$

$a_{9} = a_{1} \cdot r^{n - 1} = 61 \cdot {0.2459016393442623}^{9 - 1} = 61 \cdot {0.2459016393442623}^{8} = 61 \cdot 1.3368768175454785 E - 05 = 0.0008154948587027419$

$a_{10} = a_{1} \cdot r^{n - 1} = 61 \cdot {0.2459016393442623}^{10 - 1} = 61 \cdot {0.2459016393442623}^{9} = 61 \cdot 3.2874020103577337 E - 06 = 0.00020053152263182177$

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