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解答 - 几何数列

公比是：

r = 0.005905511811023622

r=0.005905511811023622

该系列的和是：

s = 511

s=511

此系列的通用形式是：

a_{n} = 508 \cdot {0.005905511811023622}^{n - 1}

a_n=508*0.005905511811023622^(n-1)

这个序列的第n项是：

508, 3, 0.017716535433070862, 0.00010462520925041849, 6.178654089591644 E - 07, 3.6488114702312856 E - 09, 2.1548099233649323 E - 11, 1.2725255452942512 E - 13, 7.514914637564477 E - 16, 4.437941715097132 E - 18

508,3,0.017716535433070862,0.00010462520925041849,6.178654089591644E-07,3.6488114702312856E-09,2.1548099233649323E-11,1.2725255452942512E-13,7.514914637564477E-16,4.437941715097132E-18

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：

$a_{2} a_{1} = \frac{3}{508} = 0.005905511811023622$

该序列的公比（ $r$ ）保持不变，并且等于两个连续项的商。
$r = 0.005905511811023622$

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： $a = 508$ 、公比： $r = 0.005905511811023622$ 和元素数目 $n = 2$ 插入几何级数求和公式：

$s_{2} = 508 * ((1 - {0.005905511811023622}^{2}) / (1 - 0.005905511811023622))$

$s_{2} = 508 * ((1 - 3.4875069750139496 E - 05) / (1 - 0.005905511811023622))$

$s_{2} = 508 * (0.9999651249302499 / (1 - 0.005905511811023622))$

$s_{2} = 508 * (0.9999651249302499 / 0.9940944881889764)$

$s_{2} = 508 \cdot 1.0059055118110236$

$s_{2} = 511$

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： $a = 508$ 和公比： $r = 0.005905511811023622$ 插入几何级数的公式：

$a_{n} = 508 \cdot {0.005905511811023622}^{n - 1}$

4. 找到第n项

使用通用公式找到第n项

$a_{1} = 508$

$a_{2} = a_{1} \cdot r^{n - 1} = 508 \cdot {0.005905511811023622}^{2 - 1} = 508 \cdot {0.005905511811023622}^{1} = 508 \cdot 0.005905511811023622 = 3$

$a_{3} = a_{1} \cdot r^{n - 1} = 508 \cdot {0.005905511811023622}^{3 - 1} = 508 \cdot {0.005905511811023622}^{2} = 508 \cdot 3.4875069750139496 E - 05 = 0.017716535433070862$

$a_{4} = a_{1} \cdot r^{n - 1} = 508 \cdot {0.005905511811023622}^{4 - 1} = 508 \cdot {0.005905511811023622}^{3} = 508 \cdot 2.0595513631972144 E - 07 = 0.00010462520925041849$

$a_{5} = a_{1} \cdot r^{n - 1} = 508 \cdot {0.005905511811023622}^{5 - 1} = 508 \cdot {0.005905511811023622}^{4} = 508 \cdot 1.2162704900770952 E - 09 = 6.178654089591644 E - 07$

$a_{6} = a_{1} \cdot r^{n - 1} = 508 \cdot {0.005905511811023622}^{6 - 1} = 508 \cdot {0.005905511811023622}^{5} = 508 \cdot 7.182699744549775 E - 12 = 3.6488114702312856 E - 09$

$a_{7} = a_{1} \cdot r^{n - 1} = 508 \cdot {0.005905511811023622}^{7 - 1} = 508 \cdot {0.005905511811023622}^{6} = 508 \cdot 4.241751817647505 E - 14 = 2.1548099233649323 E - 11$

$a_{8} = a_{1} \cdot r^{n - 1} = 508 \cdot {0.005905511811023622}^{8 - 1} = 508 \cdot {0.005905511811023622}^{7} = 508 \cdot 2.5049715458548253 E - 16 = 1.2725255452942512 E - 13$

$a_{9} = a_{1} \cdot r^{n - 1} = 508 \cdot {0.005905511811023622}^{9 - 1} = 508 \cdot {0.005905511811023622}^{8} = 508 \cdot 1.4793139050323773 E - 18 = 7.514914637564477 E - 16$

$a_{10} = a_{1} \cdot r^{n - 1} = 508 \cdot {0.005905511811023622}^{10 - 1} = 508 \cdot {0.005905511811023622}^{9} = 508 \cdot 8.73610573838018 E - 21 = 4.437941715097132 E - 18$

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