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解答 - 几何数列

公比是：

r = 0.10526315789473684

r=0.10526315789473684

该系列的和是：

s = 83

s=83

此系列的通用形式是：

a_{n} = 76 \cdot {0.10526315789473684}^{n - 1}

a_n=76*0.10526315789473684^(n-1)

这个序列的第n项是：

76, 8, 0.8421052631578946, 0.08864265927977838, 0.009330806239976671, 0.0009821901305238601, 0.00010338843479198527, 1.0882993135998448 E - 05, 1.1455782248419417 E - 06, 1.2058718156230967 E - 07

76,8,0.8421052631578946,0.08864265927977838,0.009330806239976671,0.0009821901305238601,0.00010338843479198527,1.0882993135998448E-05,1.1455782248419417E-06,1.2058718156230967E-07

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：

$a_{2} a_{1} = \frac{8}{76} = 0.10526315789473684$

该序列的公比（ $r$ ）保持不变，并且等于两个连续项的商。
$r = 0.10526315789473684$

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： $a = 76$ 、公比： $r = 0.10526315789473684$ 和元素数目 $n = 2$ 插入几何级数求和公式：

$s_{2} = 76 * ((1 - {0.10526315789473684}^{2}) / (1 - 0.10526315789473684))$

$s_{2} = 76 * ((1 - 0.011080332409972297) / (1 - 0.10526315789473684))$

$s_{2} = 76 * (0.9889196675900277 / (1 - 0.10526315789473684))$

$s_{2} = 76 * (0.9889196675900277 / 0.8947368421052632)$

$s_{2} = 76 \cdot 1.1052631578947367$

$s_{2} = 83.99999999999999$

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： $a = 76$ 和公比： $r = 0.10526315789473684$ 插入几何级数的公式：

$a_{n} = 76 \cdot {0.10526315789473684}^{n - 1}$

4. 找到第n项

使用通用公式找到第n项

$a_{1} = 76$

$a_{2} = a_{1} \cdot r^{n - 1} = 76 \cdot {0.10526315789473684}^{2 - 1} = 76 \cdot {0.10526315789473684}^{1} = 76 \cdot 0.10526315789473684 = 8$

$a_{3} = a_{1} \cdot r^{n - 1} = 76 \cdot {0.10526315789473684}^{3 - 1} = 76 \cdot {0.10526315789473684}^{2} = 76 \cdot 0.011080332409972297 = 0.8421052631578946$

$a_{4} = a_{1} \cdot r^{n - 1} = 76 \cdot {0.10526315789473684}^{4 - 1} = 76 \cdot {0.10526315789473684}^{3} = 76 \cdot 0.0011663507799970839 = 0.08864265927977838$

$a_{5} = a_{1} \cdot r^{n - 1} = 76 \cdot {0.10526315789473684}^{5 - 1} = 76 \cdot {0.10526315789473684}^{4} = 76 \cdot 0.00012277376631548252 = 0.009330806239976671$

$a_{6} = a_{1} \cdot r^{n - 1} = 76 \cdot {0.10526315789473684}^{6 - 1} = 76 \cdot {0.10526315789473684}^{5} = 76 \cdot 1.2923554348998159 E - 05 = 0.0009821901305238601$

$a_{7} = a_{1} \cdot r^{n - 1} = 76 \cdot {0.10526315789473684}^{7 - 1} = 76 \cdot {0.10526315789473684}^{6} = 76 \cdot 1.3603741419998062 E - 06 = 0.00010338843479198527$

$a_{8} = a_{1} \cdot r^{n - 1} = 76 \cdot {0.10526315789473684}^{8 - 1} = 76 \cdot {0.10526315789473684}^{7} = 76 \cdot 1.4319727810524274 E - 07 = 1.0882993135998448 E - 05$

$a_{9} = a_{1} \cdot r^{n - 1} = 76 \cdot {0.10526315789473684}^{9 - 1} = 76 \cdot {0.10526315789473684}^{8} = 76 \cdot 1.5073397695288708 E - 08 = 1.1455782248419417 E - 06$

$a_{10} = a_{1} \cdot r^{n - 1} = 76 \cdot {0.10526315789473684}^{10 - 1} = 76 \cdot {0.10526315789473684}^{9} = 76 \cdot 1.5866734416093377 E - 09 = 1.2058718156230967 E - 07$

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几何数列