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解答 - 几何数列

公比是：

r = 0.00024252223120452707

r=0.00024252223120452707

该系列的和是：

s = 12373

s=12373

此系列的通用形式是：

a_{n} = 12370 \cdot {0.00024252223120452707}^{n - 1}

a_n=12370*0.00024252223120452707^(n-1)

这个序列的第n项是：

12370, 3, 0.0007275666936135812, 1.7645109788526625 E - 07, 4.2793313957623184 E - 11, 1.0378329981638604 E - 14, 2.516975743323833 E - 18, 6.10422573158569 E - 22, 1.480410444200248 E - 25, 3.590324440259292 E - 29

12370,3,0.0007275666936135812,1.7645109788526625E-07,4.2793313957623184E-11,1.0378329981638604E-14,2.516975743323833E-18,6.10422573158569E-22,1.480410444200248E-25,3.590324440259292E-29

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：

$a_{2} a_{1} = \frac{3}{12370} = 0.00024252223120452707$

该序列的公比（ $r$ ）保持不变，并且等于两个连续项的商。
$r = 0.00024252223120452707$

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： $a = 12, 370$ 、公比： $r = 0.00024252223120452707$ 和元素数目 $n = 2$ 插入几何级数求和公式：

$s_{2} = 12370 * ((1 - {0.00024252223120452707}^{2}) / (1 - 0.00024252223120452707))$

$s_{2} = 12370 * ((1 - 5.881703262842209 E - 08) / (1 - 0.00024252223120452707))$

$s_{2} = 12370 * (0.9999999411829674 / (1 - 0.00024252223120452707))$

$s_{2} = 12370 * (0.9999999411829674 / 0.9997574777687954)$

$s_{2} = 12370 \cdot 1.0002425222312046$

$s_{2} = 12373$

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： $a = 12, 370$ 和公比： $r = 0.00024252223120452707$ 插入几何级数的公式：

$a_{n} = 12370 \cdot {0.00024252223120452707}^{n - 1}$

4. 找到第n项

使用通用公式找到第n项

$a_{1} = 12370$

$a_{2} = a_{1} \cdot r^{n - 1} = 12370 \cdot {0.00024252223120452707}^{2 - 1} = 12370 \cdot {0.00024252223120452707}^{1} = 12370 \cdot 0.00024252223120452707 = 3$

$a_{3} = a_{1} \cdot r^{n - 1} = 12370 \cdot {0.00024252223120452707}^{3 - 1} = 12370 \cdot {0.00024252223120452707}^{2} = 12370 \cdot 5.881703262842209 E - 08 = 0.0007275666936135812$

$a_{4} = a_{1} \cdot r^{n - 1} = 12370 \cdot {0.00024252223120452707}^{4 - 1} = 12370 \cdot {0.00024252223120452707}^{3} = 12370 \cdot 1.4264437985874394 E - 11 = 1.7645109788526625 E - 07$

$a_{5} = a_{1} \cdot r^{n - 1} = 12370 \cdot {0.00024252223120452707}^{5 - 1} = 12370 \cdot {0.00024252223120452707}^{4} = 12370 \cdot 3.4594433272128683 E - 15 = 4.2793313957623184 E - 11$

$a_{6} = a_{1} \cdot r^{n - 1} = 12370 \cdot {0.00024252223120452707}^{6 - 1} = 12370 \cdot {0.00024252223120452707}^{5} = 12370 \cdot 8.389919144412777 E - 19 = 1.0378329981638604 E - 14$

$a_{7} = a_{1} \cdot r^{n - 1} = 12370 \cdot {0.00024252223120452707}^{7 - 1} = 12370 \cdot {0.00024252223120452707}^{6} = 12370 \cdot 2.0347419105285633 E - 22 = 2.516975743323833 E - 18$

$a_{8} = a_{1} \cdot r^{n - 1} = 12370 \cdot {0.00024252223120452707}^{8 - 1} = 12370 \cdot {0.00024252223120452707}^{7} = 12370 \cdot 4.934701480667494 E - 26 = 6.10422573158569 E - 22$

$a_{9} = a_{1} \cdot r^{n - 1} = 12370 \cdot {0.00024252223120452707}^{9 - 1} = 12370 \cdot {0.00024252223120452707}^{8} = 12370 \cdot 1.196774813419764 E - 29 = 1.480410444200248 E - 25$

$a_{10} = a_{1} \cdot r^{n - 1} = 12370 \cdot {0.00024252223120452707}^{10 - 1} = 12370 \cdot {0.00024252223120452707}^{9} = 12370 \cdot 2.9024449799994275 E - 33 = 3.590324440259292 E - 29$

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几何数列