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解答 - 几何数列

公比是：

r = 0.05405405405405406

r=0.05405405405405406

该系列的和是：

s = 38

s=38

此系列的通用形式是：

a_{n} = 37 \cdot {0.05405405405405406}^{n - 1}

a_n=37*0.05405405405405406^(n-1)

这个序列的第n项是：

37, 2, 0.10810810810810813, 0.005843681519357196, 0.00031587467672201063, 1.7074306849838412 E - 05, 9.22935505396671 E - 07, 4.988840569711736 E - 08, 2.6966705782225597 E - 09, 1.4576597720121944 E - 10

37,2,0.10810810810810813,0.005843681519357196,0.00031587467672201063,1.7074306849838412E-05,9.22935505396671E-07,4.988840569711736E-08,2.6966705782225597E-09,1.4576597720121944E-10

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：

$a_{2} a_{1} = \frac{2}{37} = 0.05405405405405406$

该序列的公比（ $r$ ）保持不变，并且等于两个连续项的商。
$r = 0.05405405405405406$

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： $a = 37$ 、公比： $r = 0.05405405405405406$ 和元素数目 $n = 2$ 插入几何级数求和公式：

$s_{2} = 37 * ((1 - {0.05405405405405406}^{2}) / (1 - 0.05405405405405406))$

$s_{2} = 37 * ((1 - 0.002921840759678598) / (1 - 0.05405405405405406))$

$s_{2} = 37 * (0.9970781592403214 / (1 - 0.05405405405405406))$

$s_{2} = 37 * (0.9970781592403214 / 0.9459459459459459)$

$s_{2} = 37 \cdot 1.054054054054054$

$s_{2} = 38.99999999999999$

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： $a = 37$ 和公比： $r = 0.05405405405405406$ 插入几何级数的公式：

$a_{n} = 37 \cdot {0.05405405405405406}^{n - 1}$

4. 找到第n项

使用通用公式找到第n项

$a_{1} = 37$

$a_{2} = a_{1} \cdot r^{n - 1} = 37 \cdot {0.05405405405405406}^{2 - 1} = 37 \cdot {0.05405405405405406}^{1} = 37 \cdot 0.05405405405405406 = 2$

$a_{3} = a_{1} \cdot r^{n - 1} = 37 \cdot {0.05405405405405406}^{3 - 1} = 37 \cdot {0.05405405405405406}^{2} = 37 \cdot 0.002921840759678598 = 0.10810810810810813$

$a_{4} = a_{1} \cdot r^{n - 1} = 37 \cdot {0.05405405405405406}^{4 - 1} = 37 \cdot {0.05405405405405406}^{3} = 37 \cdot 0.0001579373383610053 = 0.005843681519357196$

$a_{5} = a_{1} \cdot r^{n - 1} = 37 \cdot {0.05405405405405406}^{5 - 1} = 37 \cdot {0.05405405405405406}^{4} = 37 \cdot 8.537153424919206 E - 06 = 0.00031587467672201063$

$a_{6} = a_{1} \cdot r^{n - 1} = 37 \cdot {0.05405405405405406}^{6 - 1} = 37 \cdot {0.05405405405405406}^{5} = 37 \cdot 4.614677526983355 E - 07 = 1.7074306849838412 E - 05$

$a_{7} = a_{1} \cdot r^{n - 1} = 37 \cdot {0.05405405405405406}^{7 - 1} = 37 \cdot {0.05405405405405406}^{6} = 37 \cdot 2.4944202848558675 E - 08 = 9.22935505396671 E - 07$

$a_{8} = a_{1} \cdot r^{n - 1} = 37 \cdot {0.05405405405405406}^{8 - 1} = 37 \cdot {0.05405405405405406}^{7} = 37 \cdot 1.3483352891112799 E - 09 = 4.988840569711736 E - 08$

$a_{9} = a_{1} \cdot r^{n - 1} = 37 \cdot {0.05405405405405406}^{9 - 1} = 37 \cdot {0.05405405405405406}^{8} = 37 \cdot 7.288298860060972 E - 11 = 2.6966705782225597 E - 09$

$a_{10} = a_{1} \cdot r^{n - 1} = 37 \cdot {0.05405405405405406}^{10 - 1} = 37 \cdot {0.05405405405405406}^{9} = 37 \cdot 3.9396210054383635 E - 12 = 1.4576597720121944 E - 10$

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几何数列