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解答 - 几何数列

公比是：

r = 0.14972512369433755

r=0.14972512369433755

该系列的和是：

s = 41827

s=41827

此系列的通用形式是：

a_{n} = 36380 \cdot {0.14972512369433755}^{n - 1}

a_n=36380*0.14972512369433755^(n-1)

这个序列的第n项是：

36380, 5447, 815.5527487630566, 122.10873618780565, 18.282745629878434, 2.7373863509056573, 0.4098555099885408, 0.06136566692984007, 0.009187982071655824, 0.0013756717521800242

36380,5447,815.5527487630566,122.10873618780565,18.282745629878434,2.7373863509056573,0.4098555099885408,0.06136566692984007,0.009187982071655824,0.0013756717521800242

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：

$a_{2} a_{1} = \frac{5447}{36380} = 0.14972512369433755$

该序列的公比（ $r$ ）保持不变，并且等于两个连续项的商。
$r = 0.14972512369433755$

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： $a = 36, 380$ 、公比： $r = 0.14972512369433755$ 和元素数目 $n = 2$ 插入几何级数求和公式：

$s_{2} = 36380 * ((1 - {0.14972512369433755}^{2}) / (1 - 0.14972512369433755))$

$s_{2} = 36380 * ((1 - 0.022417612665284678) / (1 - 0.14972512369433755))$

$s_{2} = 36380 * (0.9775823873347154 / (1 - 0.14972512369433755))$

$s_{2} = 36380 * (0.9775823873347154 / 0.8502748763056625)$

$s_{2} = 36380 \cdot 1.1497251236943375$

$s_{2} = 41827$

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： $a = 36, 380$ 和公比： $r = 0.14972512369433755$ 插入几何级数的公式：

$a_{n} = 36380 \cdot {0.14972512369433755}^{n - 1}$

4. 找到第n项

使用通用公式找到第n项

$a_{1} = 36380$

$a_{2} = a_{1} \cdot r^{n - 1} = 36380 \cdot {0.14972512369433755}^{2 - 1} = 36380 \cdot {0.14972512369433755}^{1} = 36380 \cdot 0.14972512369433755 = 5447$

$a_{3} = a_{1} \cdot r^{n - 1} = 36380 \cdot {0.14972512369433755}^{3 - 1} = 36380 \cdot {0.14972512369433755}^{2} = 36380 \cdot 0.022417612665284678 = 815.5527487630566$

$a_{4} = a_{1} \cdot r^{n - 1} = 36380 \cdot {0.14972512369433755}^{4 - 1} = 36380 \cdot {0.14972512369433755}^{3} = 36380 \cdot 0.0033564798292414965 = 122.10873618780565$

$a_{5} = a_{1} \cdot r^{n - 1} = 36380 \cdot {0.14972512369433755}^{5 - 1} = 36380 \cdot {0.14972512369433755}^{4} = 36380 \cdot 0.0005025493576107321 = 18.282745629878434$

$a_{6} = a_{1} \cdot r^{n - 1} = 36380 \cdot {0.14972512369433755}^{6 - 1} = 36380 \cdot {0.14972512369433755}^{5} = 36380 \cdot 7.524426473077673 E - 05 = 2.7373863509056573$

$a_{7} = a_{1} \cdot r^{n - 1} = 36380 \cdot {0.14972512369433755}^{7 - 1} = 36380 \cdot {0.14972512369433755}^{6} = 36380 \cdot 1.1265956844105025 E - 05 = 0.4098555099885408$

$a_{8} = a_{1} \cdot r^{n - 1} = 36380 \cdot {0.14972512369433755}^{8 - 1} = 36380 \cdot {0.14972512369433755}^{7} = 36380 \cdot 1.6867967820186937 E - 06 = 0.06136566692984007$

$a_{9} = a_{1} \cdot r^{n - 1} = 36380 \cdot {0.14972512369433755}^{9 - 1} = 36380 \cdot {0.14972512369433755}^{8} = 36380 \cdot 2.5255585683495943 E - 07 = 0.009187982071655824$

$a_{10} = a_{1} \cdot r^{n - 1} = 36380 \cdot {0.14972512369433755}^{10 - 1} = 36380 \cdot {0.14972512369433755}^{9} = 36380 \cdot 3.781395690434371 E - 08 = 0.0013756717521800242$

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几何数列