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 = 0.4105263157894737

r=0.4105263157894737

该系列的和是：

s = 134

s=134

此系列的通用形式是：

a_{n} = 95 \cdot {0.4105263157894737}^{n - 1}

a_n=95*0.4105263157894737^(n-1)

这个序列的第n项是：

95, 39, 16.010526315789473, 6.572742382271468, 2.6982837148272343, 1.1077164724027593, 0.454746762354817, 0.18668551296671435, 0.07663931584949327, 0.031462455980318285

95,39,16.010526315789473,6.572742382271468,2.6982837148272343,1.1077164724027593,0.454746762354817,0.18668551296671435,0.07663931584949327,0.031462455980318285

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：

$a_{2} a_{1} = \frac{39}{95} = 0.4105263157894737$

该序列的公比（ $r$ ）保持不变，并且等于两个连续项的商。
$r = 0.4105263157894737$

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： $a = 95$ 、公比： $r = 0.4105263157894737$ 和元素数目 $n = 2$ 插入几何级数求和公式：

$s_{2} = 95 * ((1 - {0.4105263157894737}^{2}) / (1 - 0.4105263157894737))$

$s_{2} = 95 * ((1 - 0.16853185595567868) / (1 - 0.4105263157894737))$

$s_{2} = 95 * (0.8314681440443213 / (1 - 0.4105263157894737))$

$s_{2} = 95 * (0.8314681440443213 / 0.5894736842105264)$

$s_{2} = 95 \cdot 1.4105263157894736$

$s_{2} = 134$

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： $a = 95$ 和公比： $r = 0.4105263157894737$ 插入几何级数的公式：

$a_{n} = 95 \cdot {0.4105263157894737}^{n - 1}$

4. 找到第n项

使用通用公式找到第n项

$a_{1} = 95$

$a_{2} = a_{1} \cdot r^{n - 1} = 95 \cdot {0.4105263157894737}^{2 - 1} = 95 \cdot {0.4105263157894737}^{1} = 95 \cdot 0.4105263157894737 = 39$

$a_{3} = a_{1} \cdot r^{n - 1} = 95 \cdot {0.4105263157894737}^{3 - 1} = 95 \cdot {0.4105263157894737}^{2} = 95 \cdot 0.16853185595567868 = 16.010526315789473$

$a_{4} = a_{1} \cdot r^{n - 1} = 95 \cdot {0.4105263157894737}^{4 - 1} = 95 \cdot {0.4105263157894737}^{3} = 95 \cdot 0.06918676191864703 = 6.572742382271468$

$a_{5} = a_{1} \cdot r^{n - 1} = 95 \cdot {0.4105263157894737}^{5 - 1} = 95 \cdot {0.4105263157894737}^{4} = 95 \cdot 0.028402986471865625 = 2.6982837148272343$

$a_{6} = a_{1} \cdot r^{n - 1} = 95 \cdot {0.4105263157894737}^{6 - 1} = 95 \cdot {0.4105263157894737}^{5} = 95 \cdot 0.011660173393713256 = 1.1077164724027593$

$a_{7} = a_{1} \cdot r^{n - 1} = 95 \cdot {0.4105263157894737}^{7 - 1} = 95 \cdot {0.4105263157894737}^{6} = 95 \cdot 0.004786808024787547 = 0.454746762354817$

$a_{8} = a_{1} \cdot r^{n - 1} = 95 \cdot {0.4105263157894737}^{8 - 1} = 95 \cdot {0.4105263157894737}^{7} = 95 \cdot 0.0019651106628075193 = 0.18668551296671435$

$a_{9} = a_{1} \cdot r^{n - 1} = 95 \cdot {0.4105263157894737}^{9 - 1} = 95 \cdot {0.4105263157894737}^{8} = 95 \cdot 0.0008067296405209817 = 0.07663931584949327$

$a_{10} = a_{1} \cdot r^{n - 1} = 95 \cdot {0.4105263157894737}^{10 - 1} = 95 \cdot {0.4105263157894737}^{9} = 95 \cdot 0.0003311837471612451 = 0.031462455980318285$

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