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解答 - 几何数列

公比是：

r = 0.1276595744680851

r=0.1276595744680851

该系列的和是：

s = 53

s=53

此系列的通用形式是：

a_{n} = 47 \cdot {0.1276595744680851}^{n - 1}

a_n=47*0.1276595744680851^(n-1)

这个序列的第n项是：

47, 5.999999999999999, 0.7659574468085105, 0.09778180172023537, 0.012482783198327919, 0.0015935467912759043, 0.0002034315052692644, 2.5969979396076306 E - 05, 3.3153165186480385 E - 06, 4.232318959976219 E - 07

47,5.999999999999999,0.7659574468085105,0.09778180172023537,0.012482783198327919,0.0015935467912759043,0.0002034315052692644,2.5969979396076306E-05,3.3153165186480385E-06,4.232318959976219E-07

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：

$a_{2} a_{1} = \frac{6}{47} = 0.1276595744680851$

该序列的公比（ $r$ ）保持不变，并且等于两个连续项的商。
$r = 0.1276595744680851$

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： $a = 47$ 、公比： $r = 0.1276595744680851$ 和元素数目 $n = 2$ 插入几何级数求和公式：

$s_{2} = 47 * ((1 - {0.1276595744680851}^{2}) / (1 - 0.1276595744680851))$

$s_{2} = 47 * ((1 - 0.016296966953372564) / (1 - 0.1276595744680851))$

$s_{2} = 47 * (0.9837030330466274 / (1 - 0.1276595744680851))$

$s_{2} = 47 * (0.9837030330466274 / 0.8723404255319149)$

$s_{2} = 47 \cdot 1.127659574468085$

$s_{2} = 53$

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： $a = 47$ 和公比： $r = 0.1276595744680851$ 插入几何级数的公式：

$a_{n} = 47 \cdot {0.1276595744680851}^{n - 1}$

4. 找到第n项

使用通用公式找到第n项

$a_{1} = 47$

$a_{2} = a_{1} \cdot r^{n - 1} = 47 \cdot {0.1276595744680851}^{2 - 1} = 47 \cdot {0.1276595744680851}^{1} = 47 \cdot 0.1276595744680851 = 5.999999999999999$

$a_{3} = a_{1} \cdot r^{n - 1} = 47 \cdot {0.1276595744680851}^{3 - 1} = 47 \cdot {0.1276595744680851}^{2} = 47 \cdot 0.016296966953372564 = 0.7659574468085105$

$a_{4} = a_{1} \cdot r^{n - 1} = 47 \cdot {0.1276595744680851}^{4 - 1} = 47 \cdot {0.1276595744680851}^{3} = 47 \cdot 0.002080463866387987 = 0.09778180172023537$

$a_{5} = a_{1} \cdot r^{n - 1} = 47 \cdot {0.1276595744680851}^{5 - 1} = 47 \cdot {0.1276595744680851}^{4} = 47 \cdot 0.00026559113187931744 = 0.012482783198327919$

$a_{6} = a_{1} \cdot r^{n - 1} = 47 \cdot {0.1276595744680851}^{6 - 1} = 47 \cdot {0.1276595744680851}^{5} = 47 \cdot 3.390525087821073 E - 05 = 0.0015935467912759043$

$a_{7} = a_{1} \cdot r^{n - 1} = 47 \cdot {0.1276595744680851}^{7 - 1} = 47 \cdot {0.1276595744680851}^{6} = 47 \cdot 4.328329899346051 E - 06 = 0.0002034315052692644$

$a_{8} = a_{1} \cdot r^{n - 1} = 47 \cdot {0.1276595744680851}^{8 - 1} = 47 \cdot {0.1276595744680851}^{7} = 47 \cdot 5.525527531080065 E - 07 = 2.5969979396076306 E - 05$

$a_{9} = a_{1} \cdot r^{n - 1} = 47 \cdot {0.1276595744680851}^{9 - 1} = 47 \cdot {0.1276595744680851}^{8} = 47 \cdot 7.053864933293698 E - 08 = 3.3153165186480385 E - 06$

$a_{10} = a_{1} \cdot r^{n - 1} = 47 \cdot {0.1276595744680851}^{10 - 1} = 47 \cdot {0.1276595744680851}^{9} = 47 \cdot 9.00493395739621 E - 09 = 4.232318959976219 E - 07$

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几何数列