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解答 - 几何数列

公比是：

r = 0.15384615384615385

r=0.15384615384615385

该系列的和是：

s = 494

s=494

此系列的通用形式是：

a_{n} = 429 \cdot {0.15384615384615385}^{n - 1}

a_n=429*0.15384615384615385^(n-1)

这个序列的第n项是：

429, 66, 10.153846153846155, 1.562130177514793, 0.2403277196176605, 0.03697349532579393, 0.005688230050122142, 0.0008751123154034067, 0.00013463266390821642, 2.0712717524340986 E - 05

429,66,10.153846153846155,1.562130177514793,0.2403277196176605,0.03697349532579393,0.005688230050122142,0.0008751123154034067,0.00013463266390821642,2.0712717524340986E-05

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：

$a_{2} a_{1} = \frac{66}{429} = 0.15384615384615385$

该序列的公比（ $r$ ）保持不变，并且等于两个连续项的商。
$r = 0.15384615384615385$

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： $a = 429$ 、公比： $r = 0.15384615384615385$ 和元素数目 $n = 2$ 插入几何级数求和公式：

$s_{2} = 429 * ((1 - {0.15384615384615385}^{2}) / (1 - 0.15384615384615385))$

$s_{2} = 429 * ((1 - 0.02366863905325444) / (1 - 0.15384615384615385))$

$s_{2} = 429 * (0.9763313609467456 / (1 - 0.15384615384615385))$

$s_{2} = 429 * (0.9763313609467456 / 0.8461538461538461)$

$s_{2} = 429 \cdot 1.1538461538461537$

$s_{2} = 494.99999999999994$

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： $a = 429$ 和公比： $r = 0.15384615384615385$ 插入几何级数的公式：

$a_{n} = 429 \cdot {0.15384615384615385}^{n - 1}$

4. 找到第n项

使用通用公式找到第n项

$a_{1} = 429$

$a_{2} = a_{1} \cdot r^{n - 1} = 429 \cdot {0.15384615384615385}^{2 - 1} = 429 \cdot {0.15384615384615385}^{1} = 429 \cdot 0.15384615384615385 = 66$

$a_{3} = a_{1} \cdot r^{n - 1} = 429 \cdot {0.15384615384615385}^{3 - 1} = 429 \cdot {0.15384615384615385}^{2} = 429 \cdot 0.02366863905325444 = 10.153846153846155$

$a_{4} = a_{1} \cdot r^{n - 1} = 429 \cdot {0.15384615384615385}^{4 - 1} = 429 \cdot {0.15384615384615385}^{3} = 429 \cdot 0.003641329085116068 = 1.562130177514793$

$a_{5} = a_{1} \cdot r^{n - 1} = 429 \cdot {0.15384615384615385}^{5 - 1} = 429 \cdot {0.15384615384615385}^{4} = 429 \cdot 0.0005602044746332413 = 0.2403277196176605$

$a_{6} = a_{1} \cdot r^{n - 1} = 429 \cdot {0.15384615384615385}^{6 - 1} = 429 \cdot {0.15384615384615385}^{5} = 429 \cdot 8.618530378972943 E - 05 = 0.03697349532579393$

$a_{7} = a_{1} \cdot r^{n - 1} = 429 \cdot {0.15384615384615385}^{7 - 1} = 429 \cdot {0.15384615384615385}^{6} = 429 \cdot 1.325927750611222 E - 05 = 0.005688230050122142$

$a_{8} = a_{1} \cdot r^{n - 1} = 429 \cdot {0.15384615384615385}^{8 - 1} = 429 \cdot {0.15384615384615385}^{7} = 429 \cdot 2.039888847094188 E - 06 = 0.0008751123154034067$

$a_{9} = a_{1} \cdot r^{n - 1} = 429 \cdot {0.15384615384615385}^{9 - 1} = 429 \cdot {0.15384615384615385}^{8} = 429 \cdot 3.1382905339910584 E - 07 = 0.00013463266390821642$

$a_{10} = a_{1} \cdot r^{n - 1} = 429 \cdot {0.15384615384615385}^{10 - 1} = 429 \cdot {0.15384615384615385}^{9} = 429 \cdot 4.828139283063167 E - 08 = 2.0712717524340986 E - 05$

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几何数列