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解答 - 几何数列

公比是：

r = 0.07339449541284404

r=0.07339449541284404

该系列的和是：

s = 117

s=117

此系列的通用形式是：

a_{n} = 109 \cdot {0.07339449541284404}^{n - 1}

a_n=109*0.07339449541284404^(n-1)

这个序列的第n项是：

109, 8, 0.5871559633027523, 0.04309401565524788, 0.0031628635343301198, 0.00023213677316184369, 1.7037561332979352 E - 05, 1.2504632170994023 E - 06, 9.177711685133227 E - 08, 6.735935181749157 E - 09

109,8,0.5871559633027523,0.04309401565524788,0.0031628635343301198,0.00023213677316184369,1.7037561332979352E-05,1.2504632170994023E-06,9.177711685133227E-08,6.735935181749157E-09

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：

$a_{2} a_{1} = \frac{8}{109} = 0.07339449541284404$

该序列的公比（ $r$ ）保持不变，并且等于两个连续项的商。
$r = 0.07339449541284404$

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： $a = 109$ 、公比： $r = 0.07339449541284404$ 和元素数目 $n = 2$ 插入几何级数求和公式：

$s_{2} = 109 * ((1 - {0.07339449541284404}^{2}) / (1 - 0.07339449541284404))$

$s_{2} = 109 * ((1 - 0.0053867519569059845) / (1 - 0.07339449541284404))$

$s_{2} = 109 * (0.994613248043094 / (1 - 0.07339449541284404))$

$s_{2} = 109 * (0.994613248043094 / 0.926605504587156)$

$s_{2} = 109 \cdot 1.073394495412844$

$s_{2} = 117$

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： $a = 109$ 和公比： $r = 0.07339449541284404$ 插入几何级数的公式：

$a_{n} = 109 \cdot {0.07339449541284404}^{n - 1}$

4. 找到第n项

使用通用公式找到第n项

$a_{1} = 109$

$a_{2} = a_{1} \cdot r^{n - 1} = 109 \cdot {0.07339449541284404}^{2 - 1} = 109 \cdot {0.07339449541284404}^{1} = 109 \cdot 0.07339449541284404 = 8$

$a_{3} = a_{1} \cdot r^{n - 1} = 109 \cdot {0.07339449541284404}^{3 - 1} = 109 \cdot {0.07339449541284404}^{2} = 109 \cdot 0.0053867519569059845 = 0.5871559633027523$

$a_{4} = a_{1} \cdot r^{n - 1} = 109 \cdot {0.07339449541284404}^{4 - 1} = 109 \cdot {0.07339449541284404}^{3} = 109 \cdot 0.00039535794179126497 = 0.04309401565524788$

$a_{5} = a_{1} \cdot r^{n - 1} = 109 \cdot {0.07339449541284404}^{5 - 1} = 109 \cdot {0.07339449541284404}^{4} = 109 \cdot 2.9017096645230457 E - 05 = 0.0031628635343301198$

$a_{6} = a_{1} \cdot r^{n - 1} = 109 \cdot {0.07339449541284404}^{6 - 1} = 109 \cdot {0.07339449541284404}^{5} = 109 \cdot 2.129695166622419 E - 06 = 0.00023213677316184369$

$a_{7} = a_{1} \cdot r^{n - 1} = 109 \cdot {0.07339449541284404}^{7 - 1} = 109 \cdot {0.07339449541284404}^{6} = 109 \cdot 1.5630790213742526 E - 07 = 1.7037561332979352 E - 05$

$a_{8} = a_{1} \cdot r^{n - 1} = 109 \cdot {0.07339449541284404}^{8 - 1} = 109 \cdot {0.07339449541284404}^{7} = 109 \cdot 1.1472139606416534 E - 08 = 1.2504632170994023 E - 06$

$a_{9} = a_{1} \cdot r^{n - 1} = 109 \cdot {0.07339449541284404}^{9 - 1} = 109 \cdot {0.07339449541284404}^{8} = 109 \cdot 8.419918977186448 E - 10 = 9.177711685133227 E - 08$

$a_{10} = a_{1} \cdot r^{n - 1} = 109 \cdot {0.07339449541284404}^{10 - 1} = 109 \cdot {0.07339449541284404}^{9} = 109 \cdot 6.179757047476291 E - 11 = 6.735935181749157 E - 09$

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几何数列