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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 = 54

s=54

此系列的通用形式是：

a_{n} = 39 \cdot {0.38461538461538464}^{n - 1}

a_n=39*0.38461538461538464^(n-1)

这个序列的第n项是：

39, 15, 5.769230769230769, 2.218934911242604, 0.8534365043240786, 0.32824480935541483, 0.12624800359823649, 0.04855692446086019, 0.01867574017725392, 0.007182976991251508

39,15,5.769230769230769,2.218934911242604,0.8534365043240786,0.32824480935541483,0.12624800359823649,0.04855692446086019,0.01867574017725392,0.007182976991251508

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：

$a_{2} a_{1} = \frac{15}{39} = 0.38461538461538464$

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： $a = 39$ 、公比： $r = 0.38461538461538464$ 和元素数目 $n = 2$ 插入几何级数求和公式：

$s_{2} = 39 * ((1 - {0.38461538461538464}^{2}) / (1 - 0.38461538461538464))$

$s_{2} = 39 * ((1 - 0.14792899408284024) / (1 - 0.38461538461538464))$

$s_{2} = 39 * (0.8520710059171598 / (1 - 0.38461538461538464))$

$s_{2} = 39 * (0.8520710059171598 / 0.6153846153846154)$

$s_{2} = 39 \cdot 1.3846153846153846$

$s_{2} = 54$

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： $a = 39$ 和公比： $r = 0.38461538461538464$ 插入几何级数的公式：

$a_{n} = 39 \cdot {0.38461538461538464}^{n - 1}$

4. 找到第n项

使用通用公式找到第n项

$a_{1} = 39$

$a_{2} = a_{1} \cdot r^{n - 1} = 39 \cdot {0.38461538461538464}^{2 - 1} = 39 \cdot {0.38461538461538464}^{1} = 39 \cdot 0.38461538461538464 = 15$

$a_{3} = a_{1} \cdot r^{n - 1} = 39 \cdot {0.38461538461538464}^{3 - 1} = 39 \cdot {0.38461538461538464}^{2} = 39 \cdot 0.14792899408284024 = 5.769230769230769$

$a_{4} = a_{1} \cdot r^{n - 1} = 39 \cdot {0.38461538461538464}^{4 - 1} = 39 \cdot {0.38461538461538464}^{3} = 39 \cdot 0.05689576695493856 = 2.218934911242604$

$a_{5} = a_{1} \cdot r^{n - 1} = 39 \cdot {0.38461538461538464}^{5 - 1} = 39 \cdot {0.38461538461538464}^{4} = 39 \cdot 0.02188298729036099 = 0.8534365043240786$

$a_{6} = a_{1} \cdot r^{n - 1} = 39 \cdot {0.38461538461538464}^{6 - 1} = 39 \cdot {0.38461538461538464}^{5} = 39 \cdot 0.008416533573215765 = 0.32824480935541483$

$a_{7} = a_{1} \cdot r^{n - 1} = 39 \cdot {0.38461538461538464}^{7 - 1} = 39 \cdot {0.38461538461538464}^{6} = 39 \cdot 0.003237128297390679 = 0.12624800359823649$

$a_{8} = a_{1} \cdot r^{n - 1} = 39 \cdot {0.38461538461538464}^{8 - 1} = 39 \cdot {0.38461538461538464}^{7} = 39 \cdot 0.0012450493451502613 = 0.04855692446086019$

$a_{9} = a_{1} \cdot r^{n - 1} = 39 \cdot {0.38461538461538464}^{9 - 1} = 39 \cdot {0.38461538461538464}^{8} = 39 \cdot 0.0004788651327501005 = 0.01867574017725392$

$a_{10} = a_{1} \cdot r^{n - 1} = 39 \cdot {0.38461538461538464}^{10 - 1} = 39 \cdot {0.38461538461538464}^{9} = 39 \cdot 0.00018417889721157713 = 0.007182976991251508$

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几何数列