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解答 - 几何数列

公比是：

r = 0.0013266509433962263

r=0.0013266509433962263

该系列的和是：

s = 6793

s=6793

此系列的通用形式是：

a_{n} = 6784 \cdot {0.0013266509433962263}^{n - 1}

a_n=6784*0.0013266509433962263^(n-1)

这个序列的第n项是：

6784, 9, 0.011939858490566037, 1.5840024530526875 E - 05, 2.1014183486842845 E - 08, 2.7878486347521465 E - 11, 3.698502021339816 E - 14, 4.906621195763318 E - 17, 6.509373638247325 E - 20, 8.635666678099341 E - 23

6784,9,0.011939858490566037,1.5840024530526875E-05,2.1014183486842845E-08,2.7878486347521465E-11,3.698502021339816E-14,4.906621195763318E-17,6.509373638247325E-20,8.635666678099341E-23

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：

$a_{2} a_{1} = \frac{9}{6784} = 0.0013266509433962263$

该序列的公比（ $r$ ）保持不变，并且等于两个连续项的商。
$r = 0.0013266509433962263$

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： $a = 6, 784$ 、公比： $r = 0.0013266509433962263$ 和元素数目 $n = 2$ 插入几何级数求和公式：

$s_{2} = 6784 * ((1 - {0.0013266509433962263}^{2}) / (1 - 0.0013266509433962263))$

$s_{2} = 6784 * ((1 - 1.7600027256140973 E - 06) / (1 - 0.0013266509433962263))$

$s_{2} = 6784 * (0.9999982399972744 / (1 - 0.0013266509433962263))$

$s_{2} = 6784 * (0.9999982399972744 / 0.9986733490566038)$

$s_{2} = 6784 \cdot 1.0013266509433962$

$s_{2} = 6793$

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： $a = 6, 784$ 和公比： $r = 0.0013266509433962263$ 插入几何级数的公式：

$a_{n} = 6784 \cdot {0.0013266509433962263}^{n - 1}$

4. 找到第n项

使用通用公式找到第n项

$a_{1} = 6784$

$a_{2} = a_{1} \cdot r^{n - 1} = 6784 \cdot {0.0013266509433962263}^{2 - 1} = 6784 \cdot {0.0013266509433962263}^{1} = 6784 \cdot 0.0013266509433962263 = 9$

$a_{3} = a_{1} \cdot r^{n - 1} = 6784 \cdot {0.0013266509433962263}^{3 - 1} = 6784 \cdot {0.0013266509433962263}^{2} = 6784 \cdot 1.7600027256140973 E - 06 = 0.011939858490566037$

$a_{4} = a_{1} \cdot r^{n - 1} = 6784 \cdot {0.0013266509433962263}^{4 - 1} = 6784 \cdot {0.0013266509433962263}^{3} = 6784 \cdot 2.334909276315872 E - 09 = 1.5840024530526875 E - 05$

$a_{5} = a_{1} \cdot r^{n - 1} = 6784 \cdot {0.0013266509433962263}^{5 - 1} = 6784 \cdot {0.0013266509433962263}^{4} = 6784 \cdot 3.0976095941690515 E - 12 = 2.1014183486842845 E - 08$

$a_{6} = a_{1} \cdot r^{n - 1} = 6784 \cdot {0.0013266509433962263}^{6 - 1} = 6784 \cdot {0.0013266509433962263}^{5} = 6784 \cdot 4.1094466903775744 E - 15 = 2.7878486347521465 E - 11$

$a_{7} = a_{1} \cdot r^{n - 1} = 6784 \cdot {0.0013266509433962263}^{7 - 1} = 6784 \cdot {0.0013266509433962263}^{6} = 6784 \cdot 5.4518013286259085 E - 18 = 3.698502021339816 E - 14$

$a_{8} = a_{1} \cdot r^{n - 1} = 6784 \cdot {0.0013266509433962263}^{8 - 1} = 6784 \cdot {0.0013266509433962263}^{7} = 6784 \cdot 7.232637375830362 E - 21 = 4.906621195763318 E - 17$

$a_{9} = a_{1} \cdot r^{n - 1} = 6784 \cdot {0.0013266509433962263}^{9 - 1} = 6784 \cdot {0.0013266509433962263}^{8} = 6784 \cdot 9.595185197888156 E - 24 = 6.509373638247325 E - 20$

$a_{10} = a_{1} \cdot r^{n - 1} = 6784 \cdot {0.0013266509433962263}^{10 - 1} = 6784 \cdot {0.0013266509433962263}^{9} = 6784 \cdot 1.272946149483983 E - 26 = 8.635666678099341 E - 23$

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几何数列