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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 = 150

s=150

此系列的通用形式是：

a_{n} = 130 \cdot {0.15384615384615385}^{n - 1}

a_n=130*0.15384615384615385^(n-1)

这个序列的第n项是：

130, 20, 3.076923076923077, 0.47337278106508884, 0.07282658170232137, 0.011204089492664826, 0.0017237060757945887, 0.00026518555012224445, 4.0797776941883756 E - 05, 6.276581067982117 E - 06

130,20,3.076923076923077,0.47337278106508884,0.07282658170232137,0.011204089492664826,0.0017237060757945887,0.00026518555012224445,4.0797776941883756E-05,6.276581067982117E-06

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：

$a_{2} a_{1} = \frac{20}{130} = 0.15384615384615385$

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： $a = 130$ 、公比： $r = 0.15384615384615385$ 和元素数目 $n = 2$ 插入几何级数求和公式：

$s_{2} = 130 * ((1 - {0.15384615384615385}^{2}) / (1 - 0.15384615384615385))$

$s_{2} = 130 * ((1 - 0.02366863905325444) / (1 - 0.15384615384615385))$

$s_{2} = 130 * (0.9763313609467456 / (1 - 0.15384615384615385))$

$s_{2} = 130 * (0.9763313609467456 / 0.8461538461538461)$

$s_{2} = 130 \cdot 1.1538461538461537$

$s_{2} = 150$

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： $a = 130$ 和公比： $r = 0.15384615384615385$ 插入几何级数的公式：

$a_{n} = 130 \cdot {0.15384615384615385}^{n - 1}$

4. 找到第n项

使用通用公式找到第n项

$a_{1} = 130$

$a_{2} = a_{1} \cdot r^{n - 1} = 130 \cdot {0.15384615384615385}^{2 - 1} = 130 \cdot {0.15384615384615385}^{1} = 130 \cdot 0.15384615384615385 = 20$

$a_{3} = a_{1} \cdot r^{n - 1} = 130 \cdot {0.15384615384615385}^{3 - 1} = 130 \cdot {0.15384615384615385}^{2} = 130 \cdot 0.02366863905325444 = 3.076923076923077$

$a_{4} = a_{1} \cdot r^{n - 1} = 130 \cdot {0.15384615384615385}^{4 - 1} = 130 \cdot {0.15384615384615385}^{3} = 130 \cdot 0.003641329085116068 = 0.47337278106508884$

$a_{5} = a_{1} \cdot r^{n - 1} = 130 \cdot {0.15384615384615385}^{5 - 1} = 130 \cdot {0.15384615384615385}^{4} = 130 \cdot 0.0005602044746332413 = 0.07282658170232137$

$a_{6} = a_{1} \cdot r^{n - 1} = 130 \cdot {0.15384615384615385}^{6 - 1} = 130 \cdot {0.15384615384615385}^{5} = 130 \cdot 8.618530378972943 E - 05 = 0.011204089492664826$

$a_{7} = a_{1} \cdot r^{n - 1} = 130 \cdot {0.15384615384615385}^{7 - 1} = 130 \cdot {0.15384615384615385}^{6} = 130 \cdot 1.325927750611222 E - 05 = 0.0017237060757945887$

$a_{8} = a_{1} \cdot r^{n - 1} = 130 \cdot {0.15384615384615385}^{8 - 1} = 130 \cdot {0.15384615384615385}^{7} = 130 \cdot 2.039888847094188 E - 06 = 0.00026518555012224445$

$a_{9} = a_{1} \cdot r^{n - 1} = 130 \cdot {0.15384615384615385}^{9 - 1} = 130 \cdot {0.15384615384615385}^{8} = 130 \cdot 3.1382905339910584 E - 07 = 4.0797776941883756 E - 05$

$a_{10} = a_{1} \cdot r^{n - 1} = 130 \cdot {0.15384615384615385}^{10 - 1} = 130 \cdot {0.15384615384615385}^{9} = 130 \cdot 4.828139283063167 E - 08 = 6.276581067982117 E - 06$

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几何数列