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解答 - 几何数列

公比是：

r = 0.010204695966285371

r=0.010204695966285371

该系列的和是：

s = 33559

s=33559

此系列的通用形式是：

a_{n} = 33220 \cdot {0.010204695966285371}^{n - 1}

a_n=33220*0.010204695966285371^(n-1)

这个序列的第n项是：

33220, 339, 3.459391932570741, 0.035302042900104795, 0.00036024661478433254, 3.6762071767576378 E - 06, 3.7514576547888 E - 08, 3.8282484797513643 E - 10, 3.9066111819256855 E - 12, 3.9865779370042364 E - 14

33220,339,3.459391932570741,0.035302042900104795,0.00036024661478433254,3.6762071767576378E-06,3.7514576547888E-08,3.8282484797513643E-10,3.9066111819256855E-12,3.9865779370042364E-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：

$a_{2} a_{1} = \frac{339}{33220} = 0.010204695966285371$

该序列的公比（ $r$ ）保持不变，并且等于两个连续项的商。
$r = 0.010204695966285371$

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： $a = 33, 220$ 、公比： $r = 0.010204695966285371$ 和元素数目 $n = 2$ 插入几何级数求和公式：

$s_{2} = 33220 * ((1 - {0.010204695966285371}^{2}) / (1 - 0.010204695966285371))$

$s_{2} = 33220 * ((1 - 0.00010413581976432092) / (1 - 0.010204695966285371))$

$s_{2} = 33220 * (0.9998958641802357 / (1 - 0.010204695966285371))$

$s_{2} = 33220 * (0.9998958641802357 / 0.9897953040337146)$

$s_{2} = 33220 \cdot 1.0102046959662854$

$s_{2} = 33559$

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： $a = 33, 220$ 和公比： $r = 0.010204695966285371$ 插入几何级数的公式：

$a_{n} = 33220 \cdot {0.010204695966285371}^{n - 1}$

4. 找到第n项

使用通用公式找到第n项

$a_{1} = 33220$

$a_{2} = a_{1} \cdot r^{n - 1} = 33220 \cdot {0.010204695966285371}^{2 - 1} = 33220 \cdot {0.010204695966285371}^{1} = 33220 \cdot 0.010204695966285371 = 339$

$a_{3} = a_{1} \cdot r^{n - 1} = 33220 \cdot {0.010204695966285371}^{3 - 1} = 33220 \cdot {0.010204695966285371}^{2} = 33220 \cdot 0.00010413581976432092 = 3.459391932570741$

$a_{4} = a_{1} \cdot r^{n - 1} = 33220 \cdot {0.010204695966285371}^{4 - 1} = 33220 \cdot {0.010204695966285371}^{3} = 33220 \cdot 1.062674379894786 E - 06 = 0.035302042900104795$

$a_{5} = a_{1} \cdot r^{n - 1} = 33220 \cdot {0.010204695966285371}^{5 - 1} = 33220 \cdot {0.010204695966285371}^{4} = 33220 \cdot 1.0844268957987132 E - 08 = 0.00036024661478433254$

$a_{6} = a_{1} \cdot r^{n - 1} = 33220 \cdot {0.010204695966285371}^{6 - 1} = 33220 \cdot {0.010204695966285371}^{5} = 33220 \cdot 1.1066246769288494 E - 10 = 3.6762071767576378 E - 06$

$a_{7} = a_{1} \cdot r^{n - 1} = 33220 \cdot {0.010204695966285371}^{7 - 1} = 33220 \cdot {0.010204695966285371}^{6} = 33220 \cdot 1.1292768376847682 E - 12 = 3.7514576547888 E - 08$

$a_{8} = a_{1} \cdot r^{n - 1} = 33220 \cdot {0.010204695966285371}^{8 - 1} = 33220 \cdot {0.010204695966285371}^{7} = 33220 \cdot 1.1523926790341253 E - 14 = 3.8282484797513643 E - 10$

$a_{9} = a_{1} \cdot r^{n - 1} = 33220 \cdot {0.010204695966285371}^{9 - 1} = 33220 \cdot {0.010204695966285371}^{8} = 33220 \cdot 1.1759816923316331 E - 16 = 3.9066111819256855 E - 12$

$a_{10} = a_{1} \cdot r^{n - 1} = 33220 \cdot {0.010204695966285371}^{10 - 1} = 33220 \cdot {0.010204695966285371}^{9} = 33220 \cdot 1.200053563216206 E - 18 = 3.9865779370042364 E - 14$

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几何数列