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解答 - 几何数列

公比是：

r = 0.04708994708994709

r=0.04708994708994709

该系列的和是：

s = 1979

s=1979

此系列的通用形式是：

a_{n} = 1890 \cdot {0.04708994708994709}^{n - 1}

a_n=1890*0.04708994708994709^(n-1)

这个序列的第n项是：

1890, 89, 4.1910052910052915, 0.19735421740712747, 0.009293399655679548, 0.0004376256980716824, 2.060777096739669 E - 05, 9.704188444964577 E - 07, 4.569697204242579 E - 08, 2.151867995648622 E - 09

1890,89,4.1910052910052915,0.19735421740712747,0.009293399655679548,0.0004376256980716824,2.060777096739669E-05,9.704188444964577E-07,4.569697204242579E-08,2.151867995648622E-09

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：

$a_{2} a_{1} = \frac{89}{1890} = 0.04708994708994709$

该序列的公比（ $r$ ）保持不变，并且等于两个连续项的商。
$r = 0.04708994708994709$

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： $a = 1, 890$ 、公比： $r = 0.04708994708994709$ 和元素数目 $n = 2$ 插入几何级数求和公式：

$s_{2} = 1890 * ((1 - {0.04708994708994709}^{2}) / (1 - 0.04708994708994709))$

$s_{2} = 1890 * ((1 - 0.0022174631169340165) / (1 - 0.04708994708994709))$

$s_{2} = 1890 * (0.997782536883066 / (1 - 0.04708994708994709))$

$s_{2} = 1890 * (0.997782536883066 / 0.9529100529100529)$

$s_{2} = 1890 \cdot 1.047089947089947$

$s_{2} = 1979$

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： $a = 1, 890$ 和公比： $r = 0.04708994708994709$ 插入几何级数的公式：

$a_{n} = 1890 \cdot {0.04708994708994709}^{n - 1}$

4. 找到第n项

使用通用公式找到第n项

$a_{1} = 1890$

$a_{2} = a_{1} \cdot r^{n - 1} = 1890 \cdot {0.04708994708994709}^{2 - 1} = 1890 \cdot {0.04708994708994709}^{1} = 1890 \cdot 0.04708994708994709 = 89$

$a_{3} = a_{1} \cdot r^{n - 1} = 1890 \cdot {0.04708994708994709}^{3 - 1} = 1890 \cdot {0.04708994708994709}^{2} = 1890 \cdot 0.0022174631169340165 = 4.1910052910052915$

$a_{4} = a_{1} \cdot r^{n - 1} = 1890 \cdot {0.04708994708994709}^{4 - 1} = 1890 \cdot {0.04708994708994709}^{3} = 1890 \cdot 0.00010442022085033199 = 0.19735421740712747$

$a_{5} = a_{1} \cdot r^{n - 1} = 1890 \cdot {0.04708994708994709}^{5 - 1} = 1890 \cdot {0.04708994708994709}^{4} = 1890 \cdot 4.9171426749627236 E - 06 = 0.009293399655679548$

$a_{6} = a_{1} \cdot r^{n - 1} = 1890 \cdot {0.04708994708994709}^{6 - 1} = 1890 \cdot {0.04708994708994709}^{5} = 1890 \cdot 2.3154798839771557 E - 07 = 0.0004376256980716824$

$a_{7} = a_{1} \cdot r^{n - 1} = 1890 \cdot {0.04708994708994709}^{7 - 1} = 1890 \cdot {0.04708994708994709}^{6} = 1890 \cdot 1.090358252243211 E - 08 = 2.060777096739669 E - 05$

$a_{8} = a_{1} \cdot r^{n - 1} = 1890 \cdot {0.04708994708994709}^{8 - 1} = 1890 \cdot {0.04708994708994709}^{7} = 1890 \cdot 5.134491240721998 E - 10 = 9.704188444964577 E - 07$

$a_{9} = a_{1} \cdot r^{n - 1} = 1890 \cdot {0.04708994708994709}^{9 - 1} = 1890 \cdot {0.04708994708994709}^{8} = 1890 \cdot 2.417829208593957 E - 11 = 4.569697204242579 E - 08$

$a_{10} = a_{1} \cdot r^{n - 1} = 1890 \cdot {0.04708994708994709}^{10 - 1} = 1890 \cdot {0.04708994708994709}^{9} = 1890 \cdot 1.138554495052181 E - 12 = 2.151867995648622 E - 09$

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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