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解答 - 几何数列

公比是：

r = 0.00024864351150943187

r=0.00024864351150943187

该系列的和是：

s = 181027

s=181027

此系列的通用形式是：

a_{n} = 180982 \cdot {0.00024864351150943187}^{n - 1}

a_n=180982*0.00024864351150943187^(n-1)

这个序列的第n项是：

180982, 45, 0.011188958017924433, 2.782061811708344 E - 06, 6.917416180994544 E - 10, 1.7199706498146474 E - 13, 4.2765954206307326 E - 17, 1.0633477026907811 E - 20, 2.6439450675252322 E - 24, 6.573997858275157 E - 28

180982,45,0.011188958017924433,2.782061811708344E-06,6.917416180994544E-10,1.7199706498146474E-13,4.2765954206307326E-17,1.0633477026907811E-20,2.6439450675252322E-24,6.573997858275157E-28

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：

$a_{2} a_{1} = \frac{45}{180982} = 0.00024864351150943187$

该序列的公比（ $r$ ）保持不变，并且等于两个连续项的商。
$r = 0.00024864351150943187$

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： $a = 180, 982$ 、公比： $r = 0.00024864351150943187$ 和元素数目 $n = 2$ 插入几何级数求和公式：

$s_{2} = 180982 * ((1 - {0.00024864351150943187}^{2}) / (1 - 0.00024864351150943187))$

$s_{2} = 180982 * ((1 - 6.182359581574098 E - 08) / (1 - 0.00024864351150943187))$

$s_{2} = 180982 * (0.9999999381764042 / (1 - 0.00024864351150943187))$

$s_{2} = 180982 * (0.9999999381764042 / 0.9997513564884906)$

$s_{2} = 180982 \cdot 1.0002486435115094$

$s_{2} = 181027$

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： $a = 180, 982$ 和公比： $r = 0.00024864351150943187$ 插入几何级数的公式：

$a_{n} = 180982 \cdot {0.00024864351150943187}^{n - 1}$

4. 找到第n项

使用通用公式找到第n项

$a_{1} = 180982$

$a_{2} = a_{1} \cdot r^{n - 1} = 180982 \cdot {0.00024864351150943187}^{2 - 1} = 180982 \cdot {0.00024864351150943187}^{1} = 180982 \cdot 0.00024864351150943187 = 45$

$a_{3} = a_{1} \cdot r^{n - 1} = 180982 \cdot {0.00024864351150943187}^{3 - 1} = 180982 \cdot {0.00024864351150943187}^{2} = 180982 \cdot 6.182359581574098 E - 08 = 0.011188958017924433$

$a_{4} = a_{1} \cdot r^{n - 1} = 180982 \cdot {0.00024864351150943187}^{4 - 1} = 180982 \cdot {0.00024864351150943187}^{3} = 180982 \cdot 1.5372035957765657 E - 11 = 2.782061811708344 E - 06$

$a_{5} = a_{1} \cdot r^{n - 1} = 180982 \cdot {0.00024864351150943187}^{5 - 1} = 180982 \cdot {0.00024864351150943187}^{4} = 180982 \cdot 3.822156999588105 E - 15 = 6.917416180994544 E - 10$

$a_{6} = a_{1} \cdot r^{n - 1} = 180982 \cdot {0.00024864351150943187}^{6 - 1} = 180982 \cdot {0.00024864351150943187}^{5} = 180982 \cdot 9.503545379179407 E - 19 = 1.7199706498146474 E - 13$

$a_{7} = a_{1} \cdot r^{n - 1} = 180982 \cdot {0.00024864351150943187}^{7 - 1} = 180982 \cdot {0.00024864351150943187}^{6} = 180982 \cdot 2.362994894868403 E - 22 = 4.2765954206307326 E - 17$

$a_{8} = a_{1} \cdot r^{n - 1} = 180982 \cdot {0.00024864351150943187}^{8 - 1} = 180982 \cdot {0.00024864351150943187}^{7} = 180982 \cdot 5.875433483389404 E - 26 = 1.0633477026907811 E - 20$

$a_{9} = a_{1} \cdot r^{n - 1} = 180982 \cdot {0.00024864351150943187}^{9 - 1} = 180982 \cdot {0.00024864351150943187}^{8} = 180982 \cdot 1.460888412950035 E - 29 = 2.6439450675252322 E - 24$

$a_{10} = a_{1} \cdot r^{n - 1} = 180982 \cdot {0.00024864351150943187}^{10 - 1} = 180982 \cdot {0.00024864351150943187}^{9} = 180982 \cdot 3.6324042491933766 E - 33 = 6.573997858275157 E - 28$

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几何数列