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解答 - 几何数列

公比是：

r = 0.38461538461538464

r=0.38461538461538464

该系列的和是：

s = 126

s=126

此系列的通用形式是：

a_{n} = 91 \cdot {0.38461538461538464}^{n - 1}

a_n=91*0.38461538461538464^(n-1)

这个序列的第n项是：

91, 35, 13.461538461538462, 5.177514792899409, 1.9913518434228499, 0.7659045551626347, 0.2945786750625518, 0.11329949040867378, 0.04357672708025914, 0.01676027964625352

91,35,13.461538461538462,5.177514792899409,1.9913518434228499,0.7659045551626347,0.2945786750625518,0.11329949040867378,0.04357672708025914,0.01676027964625352

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：

$a_{2} a_{1} = \frac{35}{91} = 0.38461538461538464$

该序列的公比（ $r$ ）保持不变，并且等于两个连续项的商。
$r = 0.38461538461538464$

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： $a = 91$ 、公比： $r = 0.38461538461538464$ 和元素数目 $n = 2$ 插入几何级数求和公式：

$s_{2} = 91 * ((1 - {0.38461538461538464}^{2}) / (1 - 0.38461538461538464))$

$s_{2} = 91 * ((1 - 0.14792899408284024) / (1 - 0.38461538461538464))$

$s_{2} = 91 * (0.8520710059171598 / (1 - 0.38461538461538464))$

$s_{2} = 91 * (0.8520710059171598 / 0.6153846153846154)$

$s_{2} = 91 \cdot 1.3846153846153846$

$s_{2} = 126$

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： $a = 91$ 和公比： $r = 0.38461538461538464$ 插入几何级数的公式：

$a_{n} = 91 \cdot {0.38461538461538464}^{n - 1}$

4. 找到第n项

使用通用公式找到第n项

$a_{1} = 91$

$a_{2} = a_{1} \cdot r^{n - 1} = 91 \cdot {0.38461538461538464}^{2 - 1} = 91 \cdot {0.38461538461538464}^{1} = 91 \cdot 0.38461538461538464 = 35$

$a_{3} = a_{1} \cdot r^{n - 1} = 91 \cdot {0.38461538461538464}^{3 - 1} = 91 \cdot {0.38461538461538464}^{2} = 91 \cdot 0.14792899408284024 = 13.461538461538462$

$a_{4} = a_{1} \cdot r^{n - 1} = 91 \cdot {0.38461538461538464}^{4 - 1} = 91 \cdot {0.38461538461538464}^{3} = 91 \cdot 0.05689576695493856 = 5.177514792899409$

$a_{5} = a_{1} \cdot r^{n - 1} = 91 \cdot {0.38461538461538464}^{5 - 1} = 91 \cdot {0.38461538461538464}^{4} = 91 \cdot 0.02188298729036099 = 1.9913518434228499$

$a_{6} = a_{1} \cdot r^{n - 1} = 91 \cdot {0.38461538461538464}^{6 - 1} = 91 \cdot {0.38461538461538464}^{5} = 91 \cdot 0.008416533573215765 = 0.7659045551626347$

$a_{7} = a_{1} \cdot r^{n - 1} = 91 \cdot {0.38461538461538464}^{7 - 1} = 91 \cdot {0.38461538461538464}^{6} = 91 \cdot 0.003237128297390679 = 0.2945786750625518$

$a_{8} = a_{1} \cdot r^{n - 1} = 91 \cdot {0.38461538461538464}^{8 - 1} = 91 \cdot {0.38461538461538464}^{7} = 91 \cdot 0.0012450493451502613 = 0.11329949040867378$

$a_{9} = a_{1} \cdot r^{n - 1} = 91 \cdot {0.38461538461538464}^{9 - 1} = 91 \cdot {0.38461538461538464}^{8} = 91 \cdot 0.0004788651327501005 = 0.04357672708025914$

$a_{10} = a_{1} \cdot r^{n - 1} = 91 \cdot {0.38461538461538464}^{10 - 1} = 91 \cdot {0.38461538461538464}^{9} = 91 \cdot 0.00018417889721157713 = 0.01676027964625352$

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几何数列