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解答 - 几何数列

公比是：

r = 0.1346153846153846

r=0.1346153846153846

该系列的和是：

s = 59

s=59

此系列的通用形式是：

a_{n} = 52 \cdot {0.1346153846153846}^{n - 1}

a_n=52*0.1346153846153846^(n-1)

这个序列的第n项是：

52, 7, 0.9423076923076923, 0.12684911242603547, 0.01707584205735093, 0.0022986710461818556, 0.000309436486986019, 4.1654911709656404 E - 05, 5.6073919609152855 E - 06, 7.548412255078268 E - 07

52,7,0.9423076923076923,0.12684911242603547,0.01707584205735093,0.0022986710461818556,0.000309436486986019,4.1654911709656404E-05,5.6073919609152855E-06,7.548412255078268E-07

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：

$a_{2} a_{1} = \frac{7}{52} = 0.1346153846153846$

该序列的公比（ $r$ ）保持不变，并且等于两个连续项的商。
$r = 0.1346153846153846$

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： $a = 52$ 、公比： $r = 0.1346153846153846$ 和元素数目 $n = 2$ 插入几何级数求和公式：

$s_{2} = 52 * ((1 - {0.1346153846153846}^{2}) / (1 - 0.1346153846153846))$

$s_{2} = 52 * ((1 - 0.018121301775147928) / (1 - 0.1346153846153846))$

$s_{2} = 52 * (0.9818786982248521 / (1 - 0.1346153846153846))$

$s_{2} = 52 * (0.9818786982248521 / 0.8653846153846154)$

$s_{2} = 52 \cdot 1.1346153846153846$

$s_{2} = 59$

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： $a = 52$ 和公比： $r = 0.1346153846153846$ 插入几何级数的公式：

$a_{n} = 52 \cdot {0.1346153846153846}^{n - 1}$

4. 找到第n项

使用通用公式找到第n项

$a_{1} = 52$

$a_{2} = a_{1} \cdot r^{n - 1} = 52 \cdot {0.1346153846153846}^{2 - 1} = 52 \cdot {0.1346153846153846}^{1} = 52 \cdot 0.1346153846153846 = 7$

$a_{3} = a_{1} \cdot r^{n - 1} = 52 \cdot {0.1346153846153846}^{3 - 1} = 52 \cdot {0.1346153846153846}^{2} = 52 \cdot 0.018121301775147928 = 0.9423076923076923$

$a_{4} = a_{1} \cdot r^{n - 1} = 52 \cdot {0.1346153846153846}^{4 - 1} = 52 \cdot {0.1346153846153846}^{3} = 52 \cdot 0.00243940600819299 = 0.12684911242603547$

$a_{5} = a_{1} \cdot r^{n - 1} = 52 \cdot {0.1346153846153846}^{5 - 1} = 52 \cdot {0.1346153846153846}^{4} = 52 \cdot 0.00032838157802597944 = 0.01707584205735093$

$a_{6} = a_{1} \cdot r^{n - 1} = 52 \cdot {0.1346153846153846}^{6 - 1} = 52 \cdot {0.1346153846153846}^{5} = 52 \cdot 4.420521242657415 E - 05 = 0.0022986710461818556$

$a_{7} = a_{1} \cdot r^{n - 1} = 52 \cdot {0.1346153846153846}^{7 - 1} = 52 \cdot {0.1346153846153846}^{6} = 52 \cdot 5.950701672808058 E - 06 = 0.000309436486986019$

$a_{8} = a_{1} \cdot r^{n - 1} = 52 \cdot {0.1346153846153846}^{8 - 1} = 52 \cdot {0.1346153846153846}^{7} = 52 \cdot 8.010559944164693 E - 07 = 4.1654911709656404 E - 05$

$a_{9} = a_{1} \cdot r^{n - 1} = 52 \cdot {0.1346153846153846}^{9 - 1} = 52 \cdot {0.1346153846153846}^{8} = 52 \cdot 1.0783446078683241 E - 07 = 5.6073919609152855 E - 06$

$a_{10} = a_{1} \cdot r^{n - 1} = 52 \cdot {0.1346153846153846}^{10 - 1} = 52 \cdot {0.1346153846153846}^{9} = 52 \cdot 1.4516177413612054 E - 08 = 7.548412255078268 E - 07$

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几何数列