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解答 - 几何数列

公比是：

r = - 0.022727272727272728

r=-0.022727272727272728

该系列的和是：

s = - 731

s=-731

此系列的通用形式是：

a_{n} = - 748 \cdot - {0.022727272727272728}^{n - 1}

a_n=-748*-0.022727272727272728^(n-1)

这个序列的第n项是：

- 748, 17, - 0.38636363636363635, 0.00878099173553719, - 0.00019956799398948162, 4.535636227033673 E - 06, - 1.0308264152349257 E - 07, 2.342787307352104 E - 09, - 5.324516607618418 E - 11, 1.2101174108223679 E - 12

-748,17,-0.38636363636363635,0.00878099173553719,-0.00019956799398948162,4.535636227033673E-06,-1.0308264152349257E-07,2.342787307352104E-09,-5.324516607618418E-11,1.2101174108223679E-12

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：

$a_{2} a_{1} = \frac{17}{-} 748 = - 0.022727272727272728$

该序列的公比（ $r$ ）保持不变，并且等于两个连续项的商。
$r = - 0.022727272727272728$

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： $a = - 748$ 、公比： $r = - 0.022727272727272728$ 和元素数目 $n = 2$ 插入几何级数求和公式：

$s_{2} = - 748 * ((1 - - {0.022727272727272728}^{2}) / (1 - - 0.022727272727272728))$

$s_{2} = - 748 * ((1 - 0.0005165289256198347) / (1 - - 0.022727272727272728))$

$s_{2} = - 748 * (0.9994834710743802 / (1 - - 0.022727272727272728))$

$s_{2} = - 748 * (0.9994834710743802 / 1.0227272727272727)$

$s_{2} = - 748 \cdot 0.9772727272727273$

$s_{2} = - 731$

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： $a = - 748$ 和公比： $r = - 0.022727272727272728$ 插入几何级数的公式：

$a_{n} = - 748 \cdot - {0.022727272727272728}^{n - 1}$

4. 找到第n项

使用通用公式找到第n项

$a_{1} = - 748$

$a_{2} = a_{1} \cdot r^{n - 1} = - 748 \cdot - {0.022727272727272728}^{2 - 1} = - 748 \cdot - {0.022727272727272728}^{1} = - 748 \cdot - 0.022727272727272728 = 17$

$a_{3} = a_{1} \cdot r^{n - 1} = - 748 \cdot - {0.022727272727272728}^{3 - 1} = - 748 \cdot - {0.022727272727272728}^{2} = - 748 \cdot 0.0005165289256198347 = - 0.38636363636363635$

$a_{4} = a_{1} \cdot r^{n - 1} = - 748 \cdot - {0.022727272727272728}^{4 - 1} = - 748 \cdot - {0.022727272727272728}^{3} = - 748 \cdot - 1.1739293764087153 E - 05 = 0.00878099173553719$

$a_{5} = a_{1} \cdot r^{n - 1} = - 748 \cdot - {0.022727272727272728}^{5 - 1} = - 748 \cdot - {0.022727272727272728}^{4} = - 748 \cdot 2.6680213100198077 E - 07 = - 0.00019956799398948162$

$a_{6} = a_{1} \cdot r^{n - 1} = - 748 \cdot - {0.022727272727272728}^{6 - 1} = - 748 \cdot - {0.022727272727272728}^{5} = - 748 \cdot - 6.063684795499563 E - 09 = 4.535636227033673 E - 06$

$a_{7} = a_{1} \cdot r^{n - 1} = - 748 \cdot - {0.022727272727272728}^{7 - 1} = - 748 \cdot - {0.022727272727272728}^{6} = - 748 \cdot 1.3781101807953553 E - 10 = - 1.0308264152349257 E - 07$

$a_{8} = a_{1} \cdot r^{n - 1} = - 748 \cdot - {0.022727272727272728}^{8 - 1} = - 748 \cdot - {0.022727272727272728}^{7} = - 748 \cdot - 3.1320685927167167 E - 12 = 2.342787307352104 E - 09$

$a_{9} = a_{1} \cdot r^{n - 1} = - 748 \cdot - {0.022727272727272728}^{9 - 1} = - 748 \cdot - {0.022727272727272728}^{8} = - 748 \cdot 7.11833771071981 E - 14 = - 5.324516607618418 E - 11$

$a_{10} = a_{1} \cdot r^{n - 1} = - 748 \cdot - {0.022727272727272728}^{10 - 1} = - 748 \cdot - {0.022727272727272728}^{9} = - 748 \cdot - 1.6178040251635934 E - 15 = 1.2101174108223679 E - 12$

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几何数列