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解答 - 几何数列

公比是：

r = 0.24752475247524752

r=0.24752475247524752

该系列的和是：

s = 126

s=126

此系列的通用形式是：

a_{n} = 101 \cdot {0.24752475247524752}^{n - 1}

a_n=101*0.24752475247524752^(n-1)

这个序列的第n项是：

101, 25, 6.188118811881187, 1.5317125771983138, 0.3791367765342361, 0.09384573676590002, 0.02322914276383664, 0.005749787812830851, 0.0014232148051561513, 0.00035228089236538396

101,25,6.188118811881187,1.5317125771983138,0.3791367765342361,0.09384573676590002,0.02322914276383664,0.005749787812830851,0.0014232148051561513,0.00035228089236538396

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：

$a_{2} a_{1} = \frac{25}{101} = 0.24752475247524752$

该序列的公比（ $r$ ）保持不变，并且等于两个连续项的商。
$r = 0.24752475247524752$

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： $a = 101$ 、公比： $r = 0.24752475247524752$ 和元素数目 $n = 2$ 插入几何级数求和公式：

$s_{2} = 101 * ((1 - {0.24752475247524752}^{2}) / (1 - 0.24752475247524752))$

$s_{2} = 101 * ((1 - 0.06126850308793255) / (1 - 0.24752475247524752))$

$s_{2} = 101 * (0.9387314969120675 / (1 - 0.24752475247524752))$

$s_{2} = 101 * (0.9387314969120675 / 0.7524752475247525)$

$s_{2} = 101 \cdot 1.2475247524752475$

$s_{2} = 126$

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： $a = 101$ 和公比： $r = 0.24752475247524752$ 插入几何级数的公式：

$a_{n} = 101 \cdot {0.24752475247524752}^{n - 1}$

4. 找到第n项

使用通用公式找到第n项

$a_{1} = 101$

$a_{2} = a_{1} \cdot r^{n - 1} = 101 \cdot {0.24752475247524752}^{2 - 1} = 101 \cdot {0.24752475247524752}^{1} = 101 \cdot 0.24752475247524752 = 25$

$a_{3} = a_{1} \cdot r^{n - 1} = 101 \cdot {0.24752475247524752}^{3 - 1} = 101 \cdot {0.24752475247524752}^{2} = 101 \cdot 0.06126850308793255 = 6.188118811881187$

$a_{4} = a_{1} \cdot r^{n - 1} = 101 \cdot {0.24752475247524752}^{4 - 1} = 101 \cdot {0.24752475247524752}^{3} = 101 \cdot 0.015165471061369444 = 1.5317125771983138$

$a_{5} = a_{1} \cdot r^{n - 1} = 101 \cdot {0.24752475247524752}^{5 - 1} = 101 \cdot {0.24752475247524752}^{4} = 101 \cdot 0.003753829470636001 = 0.3791367765342361$

$a_{6} = a_{1} \cdot r^{n - 1} = 101 \cdot {0.24752475247524752}^{6 - 1} = 101 \cdot {0.24752475247524752}^{5} = 101 \cdot 0.0009291657105534656 = 0.09384573676590002$

$a_{7} = a_{1} \cdot r^{n - 1} = 101 \cdot {0.24752475247524752}^{7 - 1} = 101 \cdot {0.24752475247524752}^{6} = 101 \cdot 0.00022999151251323406 = 0.02322914276383664$

$a_{8} = a_{1} \cdot r^{n - 1} = 101 \cdot {0.24752475247524752}^{8 - 1} = 101 \cdot {0.24752475247524752}^{7} = 101 \cdot 5.692859220624605 E - 05 = 0.005749787812830851$

$a_{9} = a_{1} \cdot r^{n - 1} = 101 \cdot {0.24752475247524752}^{9 - 1} = 101 \cdot {0.24752475247524752}^{8} = 101 \cdot 1.409123569461536 E - 05 = 0.0014232148051561513$

$a_{10} = a_{1} \cdot r^{n - 1} = 101 \cdot {0.24752475247524752}^{10 - 1} = 101 \cdot {0.24752475247524752}^{9} = 101 \cdot 3.4879296273800392 E - 06 = 0.00035228089236538396$

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