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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 = 216

s=216

此系列的通用形式是：

a_{n} = 156 \cdot {0.38461538461538464}^{n - 1}

a_n=156*0.38461538461538464^(n-1)

这个序列的第n项是：

156, 60, 23.076923076923077, 8.875739644970416, 3.4137460172963143, 1.3129792374216593, 0.5049920143929459, 0.19422769784344077, 0.07470296070901568, 0.02873190796500603

156,60,23.076923076923077,8.875739644970416,3.4137460172963143,1.3129792374216593,0.5049920143929459,0.19422769784344077,0.07470296070901568,0.02873190796500603

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：

$a_{2} a_{1} = \frac{60}{156} = 0.38461538461538464$

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： $a = 156$ 、公比： $r = 0.38461538461538464$ 和元素数目 $n = 2$ 插入几何级数求和公式：

$s_{2} = 156 * ((1 - {0.38461538461538464}^{2}) / (1 - 0.38461538461538464))$

$s_{2} = 156 * ((1 - 0.14792899408284024) / (1 - 0.38461538461538464))$

$s_{2} = 156 * (0.8520710059171598 / (1 - 0.38461538461538464))$

$s_{2} = 156 * (0.8520710059171598 / 0.6153846153846154)$

$s_{2} = 156 \cdot 1.3846153846153846$

$s_{2} = 216$

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： $a = 156$ 和公比： $r = 0.38461538461538464$ 插入几何级数的公式：

$a_{n} = 156 \cdot {0.38461538461538464}^{n - 1}$

4. 找到第n项

使用通用公式找到第n项

$a_{1} = 156$

$a_{2} = a_{1} \cdot r^{n - 1} = 156 \cdot {0.38461538461538464}^{2 - 1} = 156 \cdot {0.38461538461538464}^{1} = 156 \cdot 0.38461538461538464 = 60$

$a_{3} = a_{1} \cdot r^{n - 1} = 156 \cdot {0.38461538461538464}^{3 - 1} = 156 \cdot {0.38461538461538464}^{2} = 156 \cdot 0.14792899408284024 = 23.076923076923077$

$a_{4} = a_{1} \cdot r^{n - 1} = 156 \cdot {0.38461538461538464}^{4 - 1} = 156 \cdot {0.38461538461538464}^{3} = 156 \cdot 0.05689576695493856 = 8.875739644970416$

$a_{5} = a_{1} \cdot r^{n - 1} = 156 \cdot {0.38461538461538464}^{5 - 1} = 156 \cdot {0.38461538461538464}^{4} = 156 \cdot 0.02188298729036099 = 3.4137460172963143$

$a_{6} = a_{1} \cdot r^{n - 1} = 156 \cdot {0.38461538461538464}^{6 - 1} = 156 \cdot {0.38461538461538464}^{5} = 156 \cdot 0.008416533573215765 = 1.3129792374216593$

$a_{7} = a_{1} \cdot r^{n - 1} = 156 \cdot {0.38461538461538464}^{7 - 1} = 156 \cdot {0.38461538461538464}^{6} = 156 \cdot 0.003237128297390679 = 0.5049920143929459$

$a_{8} = a_{1} \cdot r^{n - 1} = 156 \cdot {0.38461538461538464}^{8 - 1} = 156 \cdot {0.38461538461538464}^{7} = 156 \cdot 0.0012450493451502613 = 0.19422769784344077$

$a_{9} = a_{1} \cdot r^{n - 1} = 156 \cdot {0.38461538461538464}^{9 - 1} = 156 \cdot {0.38461538461538464}^{8} = 156 \cdot 0.0004788651327501005 = 0.07470296070901568$

$a_{10} = a_{1} \cdot r^{n - 1} = 156 \cdot {0.38461538461538464}^{10 - 1} = 156 \cdot {0.38461538461538464}^{9} = 156 \cdot 0.00018417889721157713 = 0.02873190796500603$

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几何数列