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解答 - 几何数列

公比是：

r = 0.0032404406999351912

r=0.0032404406999351912

该系列的和是：

s = 23220

s=23220

此系列的通用形式是：

a_{n} = 23145 \cdot {0.0032404406999351912}^{n - 1}

a_n=23145*0.0032404406999351912^(n-1)

这个序列的第n项是：

23145, 75, 0.24303305249513932, 0.0007875341947347355, 2.551957857209123 E - 06, 8.269468105019843 E - 09, 2.6796721014322236 E - 11, 8.683318539961839 E - 14, 2.8137778807394167 E - 16, 9.117880365325394 E - 19

23145,75,0.24303305249513932,0.0007875341947347355,2.551957857209123E-06,8.269468105019843E-09,2.6796721014322236E-11,8.683318539961839E-14,2.8137778807394167E-16,9.117880365325394E-19

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：

$a_{2} a_{1} = \frac{75}{23145} = 0.0032404406999351912$

该序列的公比（ $r$ ）保持不变，并且等于两个连续项的商。
$r = 0.0032404406999351912$

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： $a = 23, 145$ 、公比： $r = 0.0032404406999351912$ 和元素数目 $n = 2$ 插入几何级数求和公式：

$s_{2} = 23145 * ((1 - {0.0032404406999351912}^{2}) / (1 - 0.0032404406999351912))$

$s_{2} = 23145 * ((1 - 1.0500455929796471 E - 05) / (1 - 0.0032404406999351912))$

$s_{2} = 23145 * (0.9999894995440702 / (1 - 0.0032404406999351912))$

$s_{2} = 23145 * (0.9999894995440702 / 0.9967595593000648)$

$s_{2} = 23145 \cdot 1.0032404406999353$

$s_{2} = 23220.000000000004$

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： $a = 23, 145$ 和公比： $r = 0.0032404406999351912$ 插入几何级数的公式：

$a_{n} = 23145 \cdot {0.0032404406999351912}^{n - 1}$

4. 找到第n项

使用通用公式找到第n项

$a_{1} = 23145$

$a_{2} = a_{1} \cdot r^{n - 1} = 23145 \cdot {0.0032404406999351912}^{2 - 1} = 23145 \cdot {0.0032404406999351912}^{1} = 23145 \cdot 0.0032404406999351912 = 75$

$a_{3} = a_{1} \cdot r^{n - 1} = 23145 \cdot {0.0032404406999351912}^{3 - 1} = 23145 \cdot {0.0032404406999351912}^{2} = 23145 \cdot 1.0500455929796471 E - 05 = 0.24303305249513932$

$a_{4} = a_{1} \cdot r^{n - 1} = 23145 \cdot {0.0032404406999351912}^{4 - 1} = 23145 \cdot {0.0032404406999351912}^{3} = 23145 \cdot 3.402610476278831 E - 08 = 0.0007875341947347355$

$a_{5} = a_{1} \cdot r^{n - 1} = 23145 \cdot {0.0032404406999351912}^{5 - 1} = 23145 \cdot {0.0032404406999351912}^{4} = 23145 \cdot 1.1025957473359788 E - 10 = 2.551957857209123 E - 06$

$a_{6} = a_{1} \cdot r^{n - 1} = 23145 \cdot {0.0032404406999351912}^{6 - 1} = 23145 \cdot {0.0032404406999351912}^{5} = 23145 \cdot 3.572896135242965 E - 13 = 8.269468105019843 E - 09$

$a_{7} = a_{1} \cdot r^{n - 1} = 23145 \cdot {0.0032404406999351912}^{7 - 1} = 23145 \cdot {0.0032404406999351912}^{6} = 23145 \cdot 1.1577758053282452 E - 15 = 2.6796721014322236 E - 11$

$a_{8} = a_{1} \cdot r^{n - 1} = 23145 \cdot {0.0032404406999351912}^{8 - 1} = 23145 \cdot {0.0032404406999351912}^{7} = 23145 \cdot 3.751703840985889 E - 18 = 8.683318539961839 E - 14$

$a_{9} = a_{1} \cdot r^{n - 1} = 23145 \cdot {0.0032404406999351912}^{9 - 1} = 23145 \cdot {0.0032404406999351912}^{8} = 23145 \cdot 1.2157173820433858 E - 20 = 2.8137778807394167 E - 16$

$a_{10} = a_{1} \cdot r^{n - 1} = 23145 \cdot {0.0032404406999351912}^{10 - 1} = 23145 \cdot {0.0032404406999351912}^{9} = 23145 \cdot 3.939460084392047 E - 23 = 9.117880365325394 E - 19$

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几何数列