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解答 - 几何数列

公比是：

r = 0.022727272727272728

r=0.022727272727272728

该系列的和是：

s = 90

s=90

此系列的通用形式是：

a_{n} = 88 \cdot {0.022727272727272728}^{n - 1}

a_n=88*0.022727272727272728^(n-1)

这个序列的第n项是：

88, 2, 0.045454545454545456, 0.0010330578512396695, 2.3478587528174306 E - 05, 5.336042620039615 E - 07, 1.2127369590999127 E - 08, 2.7562203615907106 E - 10, 6.2641371854334334 E - 12, 1.4236675421439623 E - 13

88,2,0.045454545454545456,0.0010330578512396695,2.3478587528174306E-05,5.336042620039615E-07,1.2127369590999127E-08,2.7562203615907106E-10,6.2641371854334334E-12,1.4236675421439623E-13

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：

$a_{2} a_{1} = \frac{2}{88} = 0.022727272727272728$

该序列的公比（ $r$ ）保持不变，并且等于两个连续项的商。
$r = 0.022727272727272728$

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： $a = 88$ 、公比： $r = 0.022727272727272728$ 和元素数目 $n = 2$ 插入几何级数求和公式：

$s_{2} = 88 * ((1 - {0.022727272727272728}^{2}) / (1 - 0.022727272727272728))$

$s_{2} = 88 * ((1 - 0.0005165289256198347) / (1 - 0.022727272727272728))$

$s_{2} = 88 * (0.9994834710743802 / (1 - 0.022727272727272728))$

$s_{2} = 88 * (0.9994834710743802 / 0.9772727272727273)$

$s_{2} = 88 \cdot 1.0227272727272727$

$s_{2} = 90$

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： $a = 88$ 和公比： $r = 0.022727272727272728$ 插入几何级数的公式：

$a_{n} = 88 \cdot {0.022727272727272728}^{n - 1}$

4. 找到第n项

使用通用公式找到第n项

$a_{1} = 88$

$a_{2} = a_{1} \cdot r^{n - 1} = 88 \cdot {0.022727272727272728}^{2 - 1} = 88 \cdot {0.022727272727272728}^{1} = 88 \cdot 0.022727272727272728 = 2$

$a_{3} = a_{1} \cdot r^{n - 1} = 88 \cdot {0.022727272727272728}^{3 - 1} = 88 \cdot {0.022727272727272728}^{2} = 88 \cdot 0.0005165289256198347 = 0.045454545454545456$

$a_{4} = a_{1} \cdot r^{n - 1} = 88 \cdot {0.022727272727272728}^{4 - 1} = 88 \cdot {0.022727272727272728}^{3} = 88 \cdot 1.1739293764087153 E - 05 = 0.0010330578512396695$

$a_{5} = a_{1} \cdot r^{n - 1} = 88 \cdot {0.022727272727272728}^{5 - 1} = 88 \cdot {0.022727272727272728}^{4} = 88 \cdot 2.6680213100198077 E - 07 = 2.3478587528174306 E - 05$

$a_{6} = a_{1} \cdot r^{n - 1} = 88 \cdot {0.022727272727272728}^{6 - 1} = 88 \cdot {0.022727272727272728}^{5} = 88 \cdot 6.063684795499563 E - 09 = 5.336042620039615 E - 07$

$a_{7} = a_{1} \cdot r^{n - 1} = 88 \cdot {0.022727272727272728}^{7 - 1} = 88 \cdot {0.022727272727272728}^{6} = 88 \cdot 1.3781101807953553 E - 10 = 1.2127369590999127 E - 08$

$a_{8} = a_{1} \cdot r^{n - 1} = 88 \cdot {0.022727272727272728}^{8 - 1} = 88 \cdot {0.022727272727272728}^{7} = 88 \cdot 3.1320685927167167 E - 12 = 2.7562203615907106 E - 10$

$a_{9} = a_{1} \cdot r^{n - 1} = 88 \cdot {0.022727272727272728}^{9 - 1} = 88 \cdot {0.022727272727272728}^{8} = 88 \cdot 7.11833771071981 E - 14 = 6.2641371854334334 E - 12$

$a_{10} = a_{1} \cdot r^{n - 1} = 88 \cdot {0.022727272727272728}^{10 - 1} = 88 \cdot {0.022727272727272728}^{9} = 88 \cdot 1.6178040251635934 E - 15 = 1.4236675421439623 E - 13$

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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。

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几何数列