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解答 - 几何数列

公比是：

r = 1.1136363636363635

r=1.1136363636363635

该系列的和是：

s = 185

s=185

此系列的通用形式是：

a_{n} = 88 \cdot {1.1136363636363635}^{n - 1}

a_n=88*1.1136363636363635^(n-1)

这个序列的第n项是：

88, 97.99999999999999, 109.13636363636361, 121.53822314049583, 135.3493848610067, 150.72999677703018, 167.8584055016927, 186.9332243087032, 208.17563616196495, 231.83195845309726

88,97.99999999999999,109.13636363636361,121.53822314049583,135.3493848610067,150.72999677703018,167.8584055016927,186.9332243087032,208.17563616196495,231.83195845309726

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：

$a_{2} a_{1} = \frac{98}{88} = 1.1136363636363635$

该序列的公比（ $r$ ）保持不变，并且等于两个连续项的商。
$r = 1.1136363636363635$

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： $r = 1.1136363636363635$ 和元素数目 $n = 2$ 插入几何级数求和公式：

$s_{2} = 88 * ((1 - {1.1136363636363635}^{2}) / (1 - 1.1136363636363635))$

$s_{2} = 88 * ((1 - 1.2401859504132229) / (1 - 1.1136363636363635))$

$s_{2} = 88 * (- 0.24018595041322288 / (1 - 1.1136363636363635))$

$s_{2} = 88 * (- 0.24018595041322288 / - 0.11363636363636354)$

$s_{2} = 88 \cdot 2.1136363636363633$

$s_{2} = 185.99999999999997$

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： $r = 1.1136363636363635$ 插入几何级数的公式：

$a_{n} = 88 \cdot {1.1136363636363635}^{n - 1}$

4. 找到第n项

使用通用公式找到第n项

$a_{1} = 88$

$a_{2} = a_{1} \cdot r^{n - 1} = 88 \cdot {1.1136363636363635}^{2 - 1} = 88 \cdot {1.1136363636363635}^{1} = 88 \cdot 1.1136363636363635 = 97.99999999999999$

$a_{3} = a_{1} \cdot r^{n - 1} = 88 \cdot {1.1136363636363635}^{3 - 1} = 88 \cdot {1.1136363636363635}^{2} = 88 \cdot 1.2401859504132229 = 109.13636363636361$

$a_{4} = a_{1} \cdot r^{n - 1} = 88 \cdot {1.1136363636363635}^{4 - 1} = 88 \cdot {1.1136363636363635}^{3} = 88 \cdot 1.381116172051089 = 121.53822314049583$

$a_{5} = a_{1} \cdot r^{n - 1} = 88 \cdot {1.1136363636363635}^{5 - 1} = 88 \cdot {1.1136363636363635}^{4} = 88 \cdot 1.538061191602349 = 135.3493848610067$

$a_{6} = a_{1} \cdot r^{n - 1} = 88 \cdot {1.1136363636363635}^{6 - 1} = 88 \cdot {1.1136363636363635}^{5} = 88 \cdot 1.712840872466252 = 150.72999677703018$

$a_{7} = a_{1} \cdot r^{n - 1} = 88 \cdot {1.1136363636363635}^{7 - 1} = 88 \cdot {1.1136363636363635}^{6} = 88 \cdot 1.9074818807010534 = 167.8584055016927$

$a_{8} = a_{1} \cdot r^{n - 1} = 88 \cdot {1.1136363636363635}^{8 - 1} = 88 \cdot {1.1136363636363635}^{7} = 88 \cdot 2.1242411853261727 = 186.9332243087032$

$a_{9} = a_{1} \cdot r^{n - 1} = 88 \cdot {1.1136363636363635}^{9 - 1} = 88 \cdot {1.1136363636363635}^{8} = 88 \cdot 2.365632229113238 = 208.17563616196495$

$a_{10} = a_{1} \cdot r^{n - 1} = 88 \cdot {1.1136363636363635}^{10 - 1} = 88 \cdot {1.1136363636363635}^{9} = 88 \cdot 2.6344540733306507 = 231.83195845309726$

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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