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解答 - 几何数列

公比是：

r = 0.8846153846153846

r=0.8846153846153846

该系列的和是：

s = 196

s=196

此系列的通用形式是：

a_{n} = 104 \cdot {0.8846153846153846}^{n - 1}

a_n=104*0.8846153846153846^(n-1)

这个序列的第n项是：

104, 92, 81.38461538461537, 71.99408284023667, 63.687073281747836, 56.338564826161544, 49.83796119237367, 44.08742720863824, 39.00041637687229, 34.50036833338702

104,92,81.38461538461537,71.99408284023667,63.687073281747836,56.338564826161544,49.83796119237367,44.08742720863824,39.00041637687229,34.50036833338702

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：

$a_{2} a_{1} = \frac{92}{104} = 0.8846153846153846$

该序列的公比（ $r$ ）保持不变，并且等于两个连续项的商。
$r = 0.8846153846153846$

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： $a = 104$ 、公比： $r = 0.8846153846153846$ 和元素数目 $n = 2$ 插入几何级数求和公式：

$s_{2} = 104 * ((1 - {0.8846153846153846}^{2}) / (1 - 0.8846153846153846))$

$s_{2} = 104 * ((1 - 0.7825443786982248) / (1 - 0.8846153846153846))$

$s_{2} = 104 * (0.2174556213017752 / (1 - 0.8846153846153846))$

$s_{2} = 104 * (0.2174556213017752 / 0.11538461538461542)$

$s_{2} = 104 \cdot 1.8846153846153846$

$s_{2} = 196$

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： $a = 104$ 和公比： $r = 0.8846153846153846$ 插入几何级数的公式：

$a_{n} = 104 \cdot {0.8846153846153846}^{n - 1}$

4. 找到第n项

使用通用公式找到第n项

$a_{1} = 104$

$a_{2} = a_{1} \cdot r^{n - 1} = 104 \cdot {0.8846153846153846}^{2 - 1} = 104 \cdot {0.8846153846153846}^{1} = 104 \cdot 0.8846153846153846 = 92$

$a_{3} = a_{1} \cdot r^{n - 1} = 104 \cdot {0.8846153846153846}^{3 - 1} = 104 \cdot {0.8846153846153846}^{2} = 104 \cdot 0.7825443786982248 = 81.38461538461537$

$a_{4} = a_{1} \cdot r^{n - 1} = 104 \cdot {0.8846153846153846}^{4 - 1} = 104 \cdot {0.8846153846153846}^{3} = 104 \cdot 0.6922507965407373 = 71.99408284023667$

$a_{5} = a_{1} \cdot r^{n - 1} = 104 \cdot {0.8846153846153846}^{5 - 1} = 104 \cdot {0.8846153846153846}^{4} = 104 \cdot 0.6123757046321907 = 63.687073281747836$

$a_{6} = a_{1} \cdot r^{n - 1} = 104 \cdot {0.8846153846153846}^{6 - 1} = 104 \cdot {0.8846153846153846}^{5} = 104 \cdot 0.5417169694823225 = 56.338564826161544$

$a_{7} = a_{1} \cdot r^{n - 1} = 104 \cdot {0.8846153846153846}^{7 - 1} = 104 \cdot {0.8846153846153846}^{6} = 104 \cdot 0.47921116531128527 = 49.83796119237367$

$a_{8} = a_{1} \cdot r^{n - 1} = 104 \cdot {0.8846153846153846}^{8 - 1} = 104 \cdot {0.8846153846153846}^{7} = 104 \cdot 0.42391756931382923 = 44.08742720863824$

$a_{9} = a_{1} \cdot r^{n - 1} = 104 \cdot {0.8846153846153846}^{9 - 1} = 104 \cdot {0.8846153846153846}^{8} = 104 \cdot 0.375004003623772 = 39.00041637687229$

$a_{10} = a_{1} \cdot r^{n - 1} = 104 \cdot {0.8846153846153846}^{10 - 1} = 104 \cdot {0.8846153846153846}^{9} = 104 \cdot 0.33173431089795213 = 34.50036833338702$

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几何数列