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解答 - 几何数列

公比是：

r = - 0.004307068659741576

r=-0.004307068659741576

该系列的和是：

s = - 7860

s=-7860

此系列的通用形式是：

a_{n} = - 7894 \cdot - {0.004307068659741576}^{n - 1}

a_n=-7894*-0.004307068659741576^(n-1)

这个序列的第n项是：

- 7894, 34, - 0.14644033443121363, 0.0006307285749507554, - 2.7165912779738642 E - 06, 1.1700545154688549 E - 08, - 5.03950513376502 E - 11, 2.1705494622246097 E - 13, - 9.34870556316655 E - 16, 4.026551674026637 E - 18

-7894,34,-0.14644033443121363,0.0006307285749507554,-2.7165912779738642E-06,1.1700545154688549E-08,-5.03950513376502E-11,2.1705494622246097E-13,-9.34870556316655E-16,4.026551674026637E-18

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：

$a_{2} a_{1} = \frac{34}{-} 7894 = - 0.004307068659741576$

该序列的公比（ $r$ ）保持不变，并且等于两个连续项的商。
$r = - 0.004307068659741576$

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： $a = - 7894$ 、公比： $r = - 0.004307068659741576$ 和元素数目 $n = 2$ 插入几何级数求和公式：

$s_{2} = - 7894 * ((1 - - {0.004307068659741576}^{2}) / (1 - - 0.004307068659741576))$

$s_{2} = - 7894 * ((1 - 1.85508404397281 E - 05) / (1 - - 0.004307068659741576))$

$s_{2} = - 7894 * (0.9999814491595602 / (1 - - 0.004307068659741576))$

$s_{2} = - 7894 * (0.9999814491595602 / 1.0043070686597415)$

$s_{2} = - 7894 \cdot 0.9956929313402585$

$s_{2} = - 7860.000000000001$

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： $a = - 7894$ 和公比： $r = - 0.004307068659741576$ 插入几何级数的公式：

$a_{n} = - 7894 \cdot - {0.004307068659741576}^{n - 1}$

4. 找到第n项

使用通用公式找到第n项

$a_{1} = - 7894$

$a_{2} = a_{1} \cdot r^{n - 1} = - 7894 \cdot - {0.004307068659741576}^{2 - 1} = - 7894 \cdot - {0.004307068659741576}^{1} = - 7894 \cdot - 0.004307068659741576 = 34$

$a_{3} = a_{1} \cdot r^{n - 1} = - 7894 \cdot - {0.004307068659741576}^{3 - 1} = - 7894 \cdot - {0.004307068659741576}^{2} = - 7894 \cdot 1.85508404397281 E - 05 = - 0.14644033443121363$

$a_{4} = a_{1} \cdot r^{n - 1} = - 7894 \cdot - {0.004307068659741576}^{4 - 1} = - 7894 \cdot - {0.004307068659741576}^{3} = - 7894 \cdot - 7.989974346981953 E - 08 = 0.0006307285749507554$

$a_{5} = a_{1} \cdot r^{n - 1} = - 7894 \cdot - {0.004307068659741576}^{5 - 1} = - 7894 \cdot - {0.004307068659741576}^{4} = - 7894 \cdot 3.441336810202514 E - 10 = - 2.7165912779738642 E - 06$

$a_{6} = a_{1} \cdot r^{n - 1} = - 7894 \cdot - {0.004307068659741576}^{6 - 1} = - 7894 \cdot - {0.004307068659741576}^{5} = - 7894 \cdot - 1.4822073922838293 E - 12 = 1.1700545154688549 E - 08$

$a_{7} = a_{1} \cdot r^{n - 1} = - 7894 \cdot - {0.004307068659741576}^{7 - 1} = - 7894 \cdot - {0.004307068659741576}^{6} = - 7894 \cdot 6.38396900654297 E - 15 = - 5.03950513376502 E - 11$

$a_{8} = a_{1} \cdot r^{n - 1} = - 7894 \cdot - {0.004307068659741576}^{8 - 1} = - 7894 \cdot - {0.004307068659741576}^{7} = - 7894 \cdot - 2.749619283284279 E - 17 = 2.1705494622246097 E - 13$

$a_{9} = a_{1} \cdot r^{n - 1} = - 7894 \cdot - {0.004307068659741576}^{9 - 1} = - 7894 \cdot - {0.004307068659741576}^{8} = - 7894 \cdot 1.1842799041254814 E - 19 = - 9.34870556316655 E - 16$

$a_{10} = a_{1} \cdot r^{n - 1} = - 7894 \cdot - {0.004307068659741576}^{10 - 1} = - 7894 \cdot - {0.004307068659741576}^{9} = - 7894 \cdot - 5.10077485942062 E - 22 = 4.026551674026637 E - 18$

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