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解答 - 几何数列

公比是：

r = 0.22429906542056074

r=0.22429906542056074

该系列的和是：

s = 262

s=262

此系列的通用形式是：

a_{n} = 214 \cdot {0.22429906542056074}^{n - 1}

a_n=214*0.22429906542056074^(n-1)

这个序列的第n项是：

214, 48, 10.766355140186915, 2.4148833959297753, 0.5416560888066786, 0.12149295449869425, 0.027250756149239837, 0.006112319136278094, 0.0013709874698193856, 0.00030751120818378743

214,48,10.766355140186915,2.4148833959297753,0.5416560888066786,0.12149295449869425,0.027250756149239837,0.006112319136278094,0.0013709874698193856,0.00030751120818378743

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：

$a_{2} a_{1} = \frac{48}{214} = 0.22429906542056074$

该序列的公比（ $r$ ）保持不变，并且等于两个连续项的商。
$r = 0.22429906542056074$

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： $a = 214$ 、公比： $r = 0.22429906542056074$ 和元素数目 $n = 2$ 插入几何级数求和公式：

$s_{2} = 214 * ((1 - {0.22429906542056074}^{2}) / (1 - 0.22429906542056074))$

$s_{2} = 214 * ((1 - 0.05031007074853699) / (1 - 0.22429906542056074))$

$s_{2} = 214 * (0.949689929251463 / (1 - 0.22429906542056074))$

$s_{2} = 214 * (0.949689929251463 / 0.7757009345794392)$

$s_{2} = 214 \cdot 1.2242990654205608$

$s_{2} = 262$

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： $a = 214$ 和公比： $r = 0.22429906542056074$ 插入几何级数的公式：

$a_{n} = 214 \cdot {0.22429906542056074}^{n - 1}$

4. 找到第n项

使用通用公式找到第n项

$a_{1} = 214$

$a_{2} = a_{1} \cdot r^{n - 1} = 214 \cdot {0.22429906542056074}^{2 - 1} = 214 \cdot {0.22429906542056074}^{1} = 214 \cdot 0.22429906542056074 = 48$

$a_{3} = a_{1} \cdot r^{n - 1} = 214 \cdot {0.22429906542056074}^{3 - 1} = 214 \cdot {0.22429906542056074}^{2} = 214 \cdot 0.05031007074853699 = 10.766355140186915$

$a_{4} = a_{1} \cdot r^{n - 1} = 214 \cdot {0.22429906542056074}^{4 - 1} = 214 \cdot {0.22429906542056074}^{3} = 214 \cdot 0.011284501850139137 = 2.4148833959297753$

$a_{5} = a_{1} \cdot r^{n - 1} = 214 \cdot {0.22429906542056074}^{5 - 1} = 214 \cdot {0.22429906542056074}^{4} = 214 \cdot 0.002531103218722797 = 0.5416560888066786$

$a_{6} = a_{1} \cdot r^{n - 1} = 214 \cdot {0.22429906542056074}^{6 - 1} = 214 \cdot {0.22429906542056074}^{5} = 214 \cdot 0.0005677240864424965 = 0.12149295449869425$

$a_{7} = a_{1} \cdot r^{n - 1} = 214 \cdot {0.22429906542056074}^{7 - 1} = 214 \cdot {0.22429906542056074}^{6} = 214 \cdot 0.00012733998200579363 = 0.027250756149239837$

$a_{8} = a_{1} \cdot r^{n - 1} = 214 \cdot {0.22429906542056074}^{8 - 1} = 214 \cdot {0.22429906542056074}^{7} = 214 \cdot 2.8562238954570532 E - 05 = 0.006112319136278094$

$a_{9} = a_{1} \cdot r^{n - 1} = 214 \cdot {0.22429906542056074}^{9 - 1} = 214 \cdot {0.22429906542056074}^{8} = 214 \cdot 6.406483503828904 E - 06 = 0.0013709874698193856$

$a_{10} = a_{1} \cdot r^{n - 1} = 214 \cdot {0.22429906542056074}^{10 - 1} = 214 \cdot {0.22429906542056074}^{9} = 214 \cdot 1.4369682625410627 E - 06 = 0.00030751120818378743$

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