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解答 - 几何数列

公比是：

r = 0.004051863857374392

r=0.004051863857374392

该系列的和是：

s = 1239

s=1239

此系列的通用形式是：

a_{n} = 1234 \cdot {0.004051863857374392}^{n - 1}

a_n=1234*0.004051863857374392^(n-1)

这个序列的第n项是：

1234, 5, 0.02025931928687196, 8.208800359348444 E - 05, 3.3260941488445884 E - 07, 1.347688066792783 E - 09, 5.460648568852442 E - 12, 2.212580457395641 E - 14, 8.9650747868543 E - 17, 3.632526250751337 E - 19

1234,5,0.02025931928687196,8.208800359348444E-05,3.3260941488445884E-07,1.347688066792783E-09,5.460648568852442E-12,2.212580457395641E-14,8.9650747868543E-17,3.632526250751337E-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：

$a_{2} a_{1} = \frac{5}{1234} = 0.004051863857374392$

该序列的公比（ $r$ ）保持不变，并且等于两个连续项的商。
$r = 0.004051863857374392$

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： $a = 1, 234$ 、公比： $r = 0.004051863857374392$ 和元素数目 $n = 2$ 插入几何级数求和公式：

$s_{2} = 1234 * ((1 - {0.004051863857374392}^{2}) / (1 - 0.004051863857374392))$

$s_{2} = 1234 * ((1 - 1.641760071869689 E - 05) / (1 - 0.004051863857374392))$

$s_{2} = 1234 * (0.9999835823992813 / (1 - 0.004051863857374392))$

$s_{2} = 1234 * (0.9999835823992813 / 0.9959481361426256)$

$s_{2} = 1234 \cdot 1.0040518638573745$

$s_{2} = 1239.0000000000002$

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： $a = 1, 234$ 和公比： $r = 0.004051863857374392$ 插入几何级数的公式：

$a_{n} = 1234 \cdot {0.004051863857374392}^{n - 1}$

4. 找到第n项

使用通用公式找到第n项

$a_{1} = 1234$

$a_{2} = a_{1} \cdot r^{n - 1} = 1234 \cdot {0.004051863857374392}^{2 - 1} = 1234 \cdot {0.004051863857374392}^{1} = 1234 \cdot 0.004051863857374392 = 5$

$a_{3} = a_{1} \cdot r^{n - 1} = 1234 \cdot {0.004051863857374392}^{3 - 1} = 1234 \cdot {0.004051863857374392}^{2} = 1234 \cdot 1.641760071869689 E - 05 = 0.02025931928687196$

$a_{4} = a_{1} \cdot r^{n - 1} = 1234 \cdot {0.004051863857374392}^{4 - 1} = 1234 \cdot {0.004051863857374392}^{3} = 1234 \cdot 6.652188297689177 E - 08 = 8.208800359348444 E - 05$

$a_{5} = a_{1} \cdot r^{n - 1} = 1234 \cdot {0.004051863857374392}^{5 - 1} = 1234 \cdot {0.004051863857374392}^{4} = 1234 \cdot 2.695376133585566 E - 10 = 3.3260941488445884 E - 07$

$a_{6} = a_{1} \cdot r^{n - 1} = 1234 \cdot {0.004051863857374392}^{6 - 1} = 1234 \cdot {0.004051863857374392}^{5} = 1234 \cdot 1.0921297137704886 E - 12 = 1.347688066792783 E - 09$

$a_{7} = a_{1} \cdot r^{n - 1} = 1234 \cdot {0.004051863857374392}^{7 - 1} = 1234 \cdot {0.004051863857374392}^{6} = 1234 \cdot 4.4251609147912825 E - 15 = 5.460648568852442 E - 12$

$a_{8} = a_{1} \cdot r^{n - 1} = 1234 \cdot {0.004051863857374392}^{8 - 1} = 1234 \cdot {0.004051863857374392}^{7} = 1234 \cdot 1.79301495737086 E - 17 = 2.212580457395641 E - 14$

$a_{9} = a_{1} \cdot r^{n - 1} = 1234 \cdot {0.004051863857374392}^{9 - 1} = 1234 \cdot {0.004051863857374392}^{8} = 1234 \cdot 7.265052501502674 E - 20 = 8.9650747868543 E - 17$

$a_{10} = a_{1} \cdot r^{n - 1} = 1234 \cdot {0.004051863857374392}^{10 - 1} = 1234 \cdot {0.004051863857374392}^{9} = 1234 \cdot 2.94370036527661 E - 22 = 3.632526250751337 E - 19$

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几何数列