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解答 - 几何数列

公比是：

r = 0.009668508287292817

r=0.009668508287292817

该系列的和是：

s = 731

s=731

此系列的通用形式是：

a_{n} = 724 \cdot {0.009668508287292817}^{n - 1}

a_n=724*0.009668508287292817^(n-1)

这个序列的第n项是：

724, 7, 0.06767955801104972, 0.0006543603675101491, 6.326688636147851 E - 06, 6.116964150971679 E - 08, 5.914191858674275 E - 10, 5.718141299823194 E - 12, 5.528589654525187 E - 14, 5.34532148918181 E - 16

724,7,0.06767955801104972,0.0006543603675101491,6.326688636147851E-06,6.116964150971679E-08,5.914191858674275E-10,5.718141299823194E-12,5.528589654525187E-14,5.34532148918181E-16

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：

$a_{2} a_{1} = \frac{7}{724} = 0.009668508287292817$

该序列的公比（ $r$ ）保持不变，并且等于两个连续项的商。
$r = 0.009668508287292817$

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： $a = 724$ 、公比： $r = 0.009668508287292817$ 和元素数目 $n = 2$ 插入几何级数求和公式：

$s_{2} = 724 * ((1 - {0.009668508287292817}^{2}) / (1 - 0.009668508287292817))$

$s_{2} = 724 * ((1 - 9.348005250144989 E - 05) / (1 - 0.009668508287292817))$

$s_{2} = 724 * (0.9999065199474986 / (1 - 0.009668508287292817))$

$s_{2} = 724 * (0.9999065199474986 / 0.9903314917127072)$

$s_{2} = 724 \cdot 1.009668508287293$

$s_{2} = 731.0000000000001$

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： $a = 724$ 和公比： $r = 0.009668508287292817$ 插入几何级数的公式：

$a_{n} = 724 \cdot {0.009668508287292817}^{n - 1}$

4. 找到第n项

使用通用公式找到第n项

$a_{1} = 724$

$a_{2} = a_{1} \cdot r^{n - 1} = 724 \cdot {0.009668508287292817}^{2 - 1} = 724 \cdot {0.009668508287292817}^{1} = 724 \cdot 0.009668508287292817 = 7$

$a_{3} = a_{1} \cdot r^{n - 1} = 724 \cdot {0.009668508287292817}^{3 - 1} = 724 \cdot {0.009668508287292817}^{2} = 724 \cdot 9.348005250144989 E - 05 = 0.06767955801104972$

$a_{4} = a_{1} \cdot r^{n - 1} = 724 \cdot {0.009668508287292817}^{4 - 1} = 724 \cdot {0.009668508287292817}^{3} = 724 \cdot 9.038126623068359 E - 07 = 0.0006543603675101491$

$a_{5} = a_{1} \cdot r^{n - 1} = 724 \cdot {0.009668508287292817}^{5 - 1} = 724 \cdot {0.009668508287292817}^{4} = 724 \cdot 8.738520215673827 E - 09 = 6.326688636147851 E - 06$

$a_{6} = a_{1} \cdot r^{n - 1} = 724 \cdot {0.009668508287292817}^{6 - 1} = 724 \cdot {0.009668508287292817}^{5} = 724 \cdot 8.448845512391821 E - 11 = 6.116964150971679 E - 08$

$a_{7} = a_{1} \cdot r^{n - 1} = 724 \cdot {0.009668508287292817}^{7 - 1} = 724 \cdot {0.009668508287292817}^{6} = 724 \cdot 8.168773285461706 E - 13 = 5.914191858674275 E - 10$

$a_{8} = a_{1} \cdot r^{n - 1} = 724 \cdot {0.009668508287292817}^{8 - 1} = 724 \cdot {0.009668508287292817}^{7} = 724 \cdot 7.897985220750268 E - 15 = 5.718141299823194 E - 12$

$a_{9} = a_{1} \cdot r^{n - 1} = 724 \cdot {0.009668508287292817}^{9 - 1} = 724 \cdot {0.009668508287292817}^{8} = 724 \cdot 7.636173555974016 E - 17 = 5.528589654525187 E - 14$

$a_{10} = a_{1} \cdot r^{n - 1} = 724 \cdot {0.009668508287292817}^{10 - 1} = 724 \cdot {0.009668508287292817}^{9} = 724 \cdot 7.383040730914103 E - 19 = 5.34532148918181 E - 16$

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几何数列