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解答 - 几何数列

公比是：

r = 0.27906976744186046

r=0.27906976744186046

该系列的和是：

s = 55

s=55

此系列的通用形式是：

a_{n} = 43 \cdot {0.27906976744186046}^{n - 1}

a_n=43*0.27906976744186046^(n-1)

这个序列的第n项是：

43, 12, 3.3488372093023258, 0.934559221200649, 0.2608072245211113, 0.07278341149426362, 0.020311649719329382, 0.005668367363533782, 0.0015818699619164042, 0.0004414520823952756

43,12,3.3488372093023258,0.934559221200649,0.2608072245211113,0.07278341149426362,0.020311649719329382,0.005668367363533782,0.0015818699619164042,0.0004414520823952756

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：

$a_{2} a_{1} = \frac{12}{43} = 0.27906976744186046$

该序列的公比（ $r$ ）保持不变，并且等于两个连续项的商。
$r = 0.27906976744186046$

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： $a = 43$ 、公比： $r = 0.27906976744186046$ 和元素数目 $n = 2$ 插入几何级数求和公式：

$s_{2} = 43 * ((1 - {0.27906976744186046}^{2}) / (1 - 0.27906976744186046))$

$s_{2} = 43 * ((1 - 0.07787993510005409) / (1 - 0.27906976744186046))$

$s_{2} = 43 * (0.9221200648999459 / (1 - 0.27906976744186046))$

$s_{2} = 43 * (0.9221200648999459 / 0.7209302325581395)$

$s_{2} = 43 \cdot 1.2790697674418605$

$s_{2} = 55$

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： $a = 43$ 和公比： $r = 0.27906976744186046$ 插入几何级数的公式：

$a_{n} = 43 \cdot {0.27906976744186046}^{n - 1}$

4. 找到第n项

使用通用公式找到第n项

$a_{1} = 43$

$a_{2} = a_{1} \cdot r^{n - 1} = 43 \cdot {0.27906976744186046}^{2 - 1} = 43 \cdot {0.27906976744186046}^{1} = 43 \cdot 0.27906976744186046 = 12$

$a_{3} = a_{1} \cdot r^{n - 1} = 43 \cdot {0.27906976744186046}^{3 - 1} = 43 \cdot {0.27906976744186046}^{2} = 43 \cdot 0.07787993510005409 = 3.3488372093023258$

$a_{4} = a_{1} \cdot r^{n - 1} = 43 \cdot {0.27906976744186046}^{4 - 1} = 43 \cdot {0.27906976744186046}^{3} = 43 \cdot 0.02173393537675928 = 0.934559221200649$

$a_{5} = a_{1} \cdot r^{n - 1} = 43 \cdot {0.27906976744186046}^{5 - 1} = 43 \cdot {0.27906976744186046}^{4} = 43 \cdot 0.0060652842911886355 = 0.2608072245211113$

$a_{6} = a_{1} \cdot r^{n - 1} = 43 \cdot {0.27906976744186046}^{6 - 1} = 43 \cdot {0.27906976744186046}^{5} = 43 \cdot 0.001692637476610782 = 0.07278341149426362$

$a_{7} = a_{1} \cdot r^{n - 1} = 43 \cdot {0.27906976744186046}^{7 - 1} = 43 \cdot {0.27906976744186046}^{6} = 43 \cdot 0.00047236394696114844 = 0.020311649719329382$

$a_{8} = a_{1} \cdot r^{n - 1} = 43 \cdot {0.27906976744186046}^{8 - 1} = 43 \cdot {0.27906976744186046}^{7} = 43 \cdot 0.00013182249682636702 = 0.005668367363533782$

$a_{9} = a_{1} \cdot r^{n - 1} = 43 \cdot {0.27906976744186046}^{9 - 1} = 43 \cdot {0.27906976744186046}^{8} = 43 \cdot 3.678767353293963 E - 05 = 0.0015818699619164042$

$a_{10} = a_{1} \cdot r^{n - 1} = 43 \cdot {0.27906976744186046}^{10 - 1} = 43 \cdot {0.27906976744186046}^{9} = 43 \cdot 1.0266327497564549 E - 05 = 0.0004414520823952756$

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几何数列