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解答 - 几何数列

公比是：

r = 0.10256410256410256

r=0.10256410256410256

该系列的和是：

s = 43

s=43

此系列的通用形式是：

a_{n} = 39 \cdot {0.10256410256410256}^{n - 1}

a_n=39*0.10256410256410256^(n-1)

这个序列的第n项是：

39, 4, 0.4102564102564102, 0.042077580539118996, 0.004315649286063487, 0.00044263069600651144, 4.539802010323194 E - 05, 4.656207190075071 E - 06, 4.775597118025713 E - 07, 4.898048326180219 E - 08

39,4,0.4102564102564102,0.042077580539118996,0.004315649286063487,0.00044263069600651144,4.539802010323194E-05,4.656207190075071E-06,4.775597118025713E-07,4.898048326180219E-08

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：

$a_{2} a_{1} = \frac{4}{39} = 0.10256410256410256$

该序列的公比（ $r$ ）保持不变，并且等于两个连续项的商。
$r = 0.10256410256410256$

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： $a = 39$ 、公比： $r = 0.10256410256410256$ 和元素数目 $n = 2$ 插入几何级数求和公式：

$s_{2} = 39 * ((1 - {0.10256410256410256}^{2}) / (1 - 0.10256410256410256))$

$s_{2} = 39 * ((1 - 0.010519395134779749) / (1 - 0.10256410256410256))$

$s_{2} = 39 * (0.9894806048652203 / (1 - 0.10256410256410256))$

$s_{2} = 39 * (0.9894806048652203 / 0.8974358974358975)$

$s_{2} = 39 \cdot 1.1025641025641026$

$s_{2} = 43$

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： $a = 39$ 和公比： $r = 0.10256410256410256$ 插入几何级数的公式：

$a_{n} = 39 \cdot {0.10256410256410256}^{n - 1}$

4. 找到第n项

使用通用公式找到第n项

$a_{1} = 39$

$a_{2} = a_{1} \cdot r^{n - 1} = 39 \cdot {0.10256410256410256}^{2 - 1} = 39 \cdot {0.10256410256410256}^{1} = 39 \cdot 0.10256410256410256 = 4$

$a_{3} = a_{1} \cdot r^{n - 1} = 39 \cdot {0.10256410256410256}^{3 - 1} = 39 \cdot {0.10256410256410256}^{2} = 39 \cdot 0.010519395134779749 = 0.4102564102564102$

$a_{4} = a_{1} \cdot r^{n - 1} = 39 \cdot {0.10256410256410256}^{4 - 1} = 39 \cdot {0.10256410256410256}^{3} = 39 \cdot 0.0010789123215158717 = 0.042077580539118996$

$a_{5} = a_{1} \cdot r^{n - 1} = 39 \cdot {0.10256410256410256}^{5 - 1} = 39 \cdot {0.10256410256410256}^{4} = 39 \cdot 0.00011065767400162786 = 0.004315649286063487$

$a_{6} = a_{1} \cdot r^{n - 1} = 39 \cdot {0.10256410256410256}^{6 - 1} = 39 \cdot {0.10256410256410256}^{5} = 39 \cdot 1.1349505025807985 E - 05 = 0.00044263069600651144$

$a_{7} = a_{1} \cdot r^{n - 1} = 39 \cdot {0.10256410256410256}^{7 - 1} = 39 \cdot {0.10256410256410256}^{6} = 39 \cdot 1.1640517975187676 E - 06 = 4.539802010323194 E - 05$

$a_{8} = a_{1} \cdot r^{n - 1} = 39 \cdot {0.10256410256410256}^{8 - 1} = 39 \cdot {0.10256410256410256}^{7} = 39 \cdot 1.1938992795064285 E - 07 = 4.656207190075071 E - 06$

$a_{9} = a_{1} \cdot r^{n - 1} = 39 \cdot {0.10256410256410256}^{9 - 1} = 39 \cdot {0.10256410256410256}^{8} = 39 \cdot 1.2245120815450546 E - 08 = 4.775597118025713 E - 07$

$a_{10} = a_{1} \cdot r^{n - 1} = 39 \cdot {0.10256410256410256}^{10 - 1} = 39 \cdot {0.10256410256410256}^{9} = 39 \cdot 1.2559098272256972 E - 09 = 4.898048326180219 E - 08$

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几何数列