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解答 - 几何数列

公比是：

r = 0.01606425702811245

r=0.01606425702811245

该系列的和是：

s = 253

s=253

此系列的通用形式是：

a_{n} = 249 \cdot {0.01606425702811245}^{n - 1}

a_n=249*0.01606425702811245^(n-1)

这个序列的第n项是：

249, 3.9999999999999996, 0.06425702811244978, 0.0010322414154610407, 1.6582191413028766 E - 05, 2.663805849482532 E - 07, 4.279206183907682 E - 09, 6.874226801458122 E - 11, 1.104293462081626 E - 12, 1.7739654009343386 E - 14

249,3.9999999999999996,0.06425702811244978,0.0010322414154610407,1.6582191413028766E-05,2.663805849482532E-07,4.279206183907682E-09,6.874226801458122E-11,1.104293462081626E-12,1.7739654009343386E-14

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：

$a_{2} a_{1} = \frac{4}{249} = 0.01606425702811245$

该序列的公比（ $r$ ）保持不变，并且等于两个连续项的商。
$r = 0.01606425702811245$

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： $a = 249$ 、公比： $r = 0.01606425702811245$ 和元素数目 $n = 2$ 插入几何级数求和公式：

$s_{2} = 249 * ((1 - {0.01606425702811245}^{2}) / (1 - 0.01606425702811245))$

$s_{2} = 249 * ((1 - 0.0002580603538652602) / (1 - 0.01606425702811245))$

$s_{2} = 249 * (0.9997419396461348 / (1 - 0.01606425702811245))$

$s_{2} = 249 * (0.9997419396461348 / 0.9839357429718876)$

$s_{2} = 249 \cdot 1.0160642570281124$

$s_{2} = 253$

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： $a = 249$ 和公比： $r = 0.01606425702811245$ 插入几何级数的公式：

$a_{n} = 249 \cdot {0.01606425702811245}^{n - 1}$

4. 找到第n项

使用通用公式找到第n项

$a_{1} = 249$

$a_{2} = a_{1} \cdot r^{n - 1} = 249 \cdot {0.01606425702811245}^{2 - 1} = 249 \cdot {0.01606425702811245}^{1} = 249 \cdot 0.01606425702811245 = 3.9999999999999996$

$a_{3} = a_{1} \cdot r^{n - 1} = 249 \cdot {0.01606425702811245}^{3 - 1} = 249 \cdot {0.01606425702811245}^{2} = 249 \cdot 0.0002580603538652602 = 0.06425702811244978$

$a_{4} = a_{1} \cdot r^{n - 1} = 249 \cdot {0.01606425702811245}^{4 - 1} = 249 \cdot {0.01606425702811245}^{3} = 249 \cdot 4.145547853257192 E - 06 = 0.0010322414154610407$

$a_{5} = a_{1} \cdot r^{n - 1} = 249 \cdot {0.01606425702811245}^{5 - 1} = 249 \cdot {0.01606425702811245}^{4} = 249 \cdot 6.659514623706331 E - 08 = 1.6582191413028766 E - 05$

$a_{6} = a_{1} \cdot r^{n - 1} = 249 \cdot {0.01606425702811245}^{6 - 1} = 249 \cdot {0.01606425702811245}^{5} = 249 \cdot 1.0698015459769205 E - 09 = 2.663805849482532 E - 07$

$a_{7} = a_{1} \cdot r^{n - 1} = 249 \cdot {0.01606425702811245}^{7 - 1} = 249 \cdot {0.01606425702811245}^{6} = 249 \cdot 1.7185567003645308 E - 11 = 4.279206183907682 E - 09$

$a_{8} = a_{1} \cdot r^{n - 1} = 249 \cdot {0.01606425702811245}^{8 - 1} = 249 \cdot {0.01606425702811245}^{7} = 249 \cdot 2.760733655204065 E - 13 = 6.874226801458122 E - 11$

$a_{9} = a_{1} \cdot r^{n - 1} = 249 \cdot {0.01606425702811245}^{9 - 1} = 249 \cdot {0.01606425702811245}^{8} = 249 \cdot 4.434913502335847 E - 15 = 1.104293462081626 E - 12$

$a_{10} = a_{1} \cdot r^{n - 1} = 249 \cdot {0.01606425702811245}^{10 - 1} = 249 \cdot {0.01606425702811245}^{9} = 249 \cdot 7.124359039896943 E - 17 = 1.7739654009343386 E - 14$

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几何数列