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解答 - 几何数列

公比是：

r = 0.13684881688943465

r=0.13684881688943465

该系列的和是：

s = 48141

s=48141

此系列的通用形式是：

a_{n} = 42346 \cdot {0.13684881688943465}^{n - 1}

a_n=42346*0.13684881688943465^(n-1)

这个序列的第n项是：

42346, 5795, 793.0388938742738, 108.52643437400029, 14.85171414531081, 2.0324395095658656, 0.2781369422834315, 0.03806271148473257, 0.0052088370342895495, 0.0007128231855123964

42346,5795,793.0388938742738,108.52643437400029,14.85171414531081,2.0324395095658656,0.2781369422834315,0.03806271148473257,0.0052088370342895495,0.0007128231855123964

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：

$a_{2} a_{1} = \frac{5795}{42346} = 0.13684881688943465$

该序列的公比（ $r$ ）保持不变，并且等于两个连续项的商。
$r = 0.13684881688943465$

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： $a = 42, 346$ 、公比： $r = 0.13684881688943465$ 和元素数目 $n = 2$ 插入几何级数求和公式：

$s_{2} = 42346 * ((1 - {0.13684881688943465}^{2}) / (1 - 0.13684881688943465))$

$s_{2} = 42346 * ((1 - 0.018727598684038015) / (1 - 0.13684881688943465))$

$s_{2} = 42346 * (0.9812724013159619 / (1 - 0.13684881688943465))$

$s_{2} = 42346 * (0.9812724013159619 / 0.8631511831105654)$

$s_{2} = 42346 \cdot 1.1368488168894346$

$s_{2} = 48141$

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： $a = 42, 346$ 和公比： $r = 0.13684881688943465$ 插入几何级数的公式：

$a_{n} = 42346 \cdot {0.13684881688943465}^{n - 1}$

4. 找到第n项

使用通用公式找到第n项

$a_{1} = 42346$

$a_{2} = a_{1} \cdot r^{n - 1} = 42346 \cdot {0.13684881688943465}^{2 - 1} = 42346 \cdot {0.13684881688943465}^{1} = 42346 \cdot 0.13684881688943465 = 5795$

$a_{3} = a_{1} \cdot r^{n - 1} = 42346 \cdot {0.13684881688943465}^{3 - 1} = 42346 \cdot {0.13684881688943465}^{2} = 42346 \cdot 0.018727598684038015 = 793.0388938742738$

$a_{4} = a_{1} \cdot r^{n - 1} = 42346 \cdot {0.13684881688943465}^{4 - 1} = 42346 \cdot {0.13684881688943465}^{3} = 42346 \cdot 0.0025628497230907356 = 108.52643437400029$

$a_{5} = a_{1} \cdot r^{n - 1} = 42346 \cdot {0.13684881688943465}^{5 - 1} = 42346 \cdot {0.13684881688943465}^{4} = 42346 \cdot 0.00035072295247038233 = 14.85171414531081$

$a_{6} = a_{1} \cdot r^{n - 1} = 42346 \cdot {0.13684881688943465}^{6 - 1} = 42346 \cdot {0.13684881688943465}^{5} = 42346 \cdot 4.799602110154125 E - 05 = 2.0324395095658656$

$a_{7} = a_{1} \cdot r^{n - 1} = 42346 \cdot {0.13684881688943465}^{7 - 1} = 42346 \cdot {0.13684881688943465}^{6} = 42346 \cdot 6.56819870314626 E - 06 = 0.2781369422834315$

$a_{8} = a_{1} \cdot r^{n - 1} = 42346 \cdot {0.13684881688943465}^{8 - 1} = 42346 \cdot {0.13684881688943465}^{7} = 42346 \cdot 8.988502216202846 E - 07 = 0.03806271148473257$

$a_{9} = a_{1} \cdot r^{n - 1} = 42346 \cdot {0.13684881688943465}^{9 - 1} = 42346 \cdot {0.13684881688943465}^{8} = 42346 \cdot 1.230065893895421 E - 07 = 0.0052088370342895495$

$a_{10} = a_{1} \cdot r^{n - 1} = 42346 \cdot {0.13684881688943465}^{10 - 1} = 42346 \cdot {0.13684881688943465}^{9} = 42346 \cdot 1.683330622756332 E - 08 = 0.0007128231855123964$

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几何数列