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解答 - 几何数列

公比是：

r = 0.2755102040816326

r=0.2755102040816326

该系列的和是：

s = 125

s=125

此系列的通用形式是：

a_{n} = 98 \cdot {0.2755102040816326}^{n - 1}

a_n=98*0.2755102040816326^(n-1)

这个序列的第n项是：

98, 26.999999999999996, 7.43877551020408, 2.049458558933777, 0.5646467458286936, 0.1555659401772931, 0.042860003926397085, 0.011808368428701236, 0.003253325995662585, 0.0008963245090090795

98,26.999999999999996,7.43877551020408,2.049458558933777,0.5646467458286936,0.1555659401772931,0.042860003926397085,0.011808368428701236,0.003253325995662585,0.0008963245090090795

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：

$a_{2} a_{1} = \frac{27}{98} = 0.2755102040816326$

该序列的公比（ $r$ ）保持不变，并且等于两个连续项的商。
$r = 0.2755102040816326$

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： $a = 98$ 、公比： $r = 0.2755102040816326$ 和元素数目 $n = 2$ 插入几何级数求和公式：

$s_{2} = 98 * ((1 - {0.2755102040816326}^{2}) / (1 - 0.2755102040816326))$

$s_{2} = 98 * ((1 - 0.07590587255310285) / (1 - 0.2755102040816326))$

$s_{2} = 98 * (0.9240941274468971 / (1 - 0.2755102040816326))$

$s_{2} = 98 * (0.9240941274468971 / 0.7244897959183674)$

$s_{2} = 98 \cdot 1.2755102040816326$

$s_{2} = 125$

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： $a = 98$ 和公比： $r = 0.2755102040816326$ 插入几何级数的公式：

$a_{n} = 98 \cdot {0.2755102040816326}^{n - 1}$

4. 找到第n项

使用通用公式找到第n项

$a_{1} = 98$

$a_{2} = a_{1} \cdot r^{n - 1} = 98 \cdot {0.2755102040816326}^{2 - 1} = 98 \cdot {0.2755102040816326}^{1} = 98 \cdot 0.2755102040816326 = 26.999999999999996$

$a_{3} = a_{1} \cdot r^{n - 1} = 98 \cdot {0.2755102040816326}^{3 - 1} = 98 \cdot {0.2755102040816326}^{2} = 98 \cdot 0.07590587255310285 = 7.43877551020408$

$a_{4} = a_{1} \cdot r^{n - 1} = 98 \cdot {0.2755102040816326}^{4 - 1} = 98 \cdot {0.2755102040816326}^{3} = 98 \cdot 0.020912842438099766 = 2.049458558933777$

$a_{5} = a_{1} \cdot r^{n - 1} = 98 \cdot {0.2755102040816326}^{5 - 1} = 98 \cdot {0.2755102040816326}^{4} = 98 \cdot 0.005761701488047894 = 0.5646467458286936$

$a_{6} = a_{1} \cdot r^{n - 1} = 98 \cdot {0.2755102040816326}^{6 - 1} = 98 \cdot {0.2755102040816326}^{5} = 98 \cdot 0.0015874075528295216 = 0.1555659401772931$

$a_{7} = a_{1} \cdot r^{n - 1} = 98 \cdot {0.2755102040816326}^{7 - 1} = 98 \cdot {0.2755102040816326}^{6} = 98 \cdot 0.00043734697884078655 = 0.042860003926397085$

$a_{8} = a_{1} \cdot r^{n - 1} = 98 \cdot {0.2755102040816326}^{8 - 1} = 98 \cdot {0.2755102040816326}^{7} = 98 \cdot 0.00012049355539491056 = 0.011808368428701236$

$a_{9} = a_{1} \cdot r^{n - 1} = 98 \cdot {0.2755102040816326}^{9 - 1} = 98 \cdot {0.2755102040816326}^{8} = 98 \cdot 3.3197204037373315 E - 05 = 0.003253325995662585$

$a_{10} = a_{1} \cdot r^{n - 1} = 98 \cdot {0.2755102040816326}^{10 - 1} = 98 \cdot {0.2755102040816326}^{9} = 98 \cdot 9.14616845927632 E - 06 = 0.0008963245090090795$

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