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解答 - 几何数列

公比是：

r = 0.02459016393442623

r=0.02459016393442623

该系列的和是：

s = 124

s=124

此系列的通用形式是：

a_{n} = 122 \cdot {0.02459016393442623}^{n - 1}

a_n=122*0.02459016393442623^(n-1)

这个序列的第n项是：

122, 3, 0.07377049180327869, 0.0018140284869658694, 4.46072578762099 E - 05, 1.0968997838412272 E - 06, 2.6972945504292465 E - 08, 6.632691517448967 E - 10, 1.6309897174054836 E - 11, 4.0106304526364353 E - 13

122,3,0.07377049180327869,0.0018140284869658694,4.46072578762099E-05,1.0968997838412272E-06,2.6972945504292465E-08,6.632691517448967E-10,1.6309897174054836E-11,4.0106304526364353E-13

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：

$a_{2} a_{1} = \frac{3}{122} = 0.02459016393442623$

该序列的公比（ $r$ ）保持不变，并且等于两个连续项的商。
$r = 0.02459016393442623$

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： $a = 122$ 、公比： $r = 0.02459016393442623$ 和元素数目 $n = 2$ 插入几何级数求和公式：

$s_{2} = 122 * ((1 - {0.02459016393442623}^{2}) / (1 - 0.02459016393442623))$

$s_{2} = 122 * ((1 - 0.0006046761623219564) / (1 - 0.02459016393442623))$

$s_{2} = 122 * (0.999395323837678 / (1 - 0.02459016393442623))$

$s_{2} = 122 * (0.999395323837678 / 0.9754098360655737)$

$s_{2} = 122 \cdot 1.0245901639344261$

$s_{2} = 124.99999999999999$

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： $a = 122$ 和公比： $r = 0.02459016393442623$ 插入几何级数的公式：

$a_{n} = 122 \cdot {0.02459016393442623}^{n - 1}$

4. 找到第n项

使用通用公式找到第n项

$a_{1} = 122$

$a_{2} = a_{1} \cdot r^{n - 1} = 122 \cdot {0.02459016393442623}^{2 - 1} = 122 \cdot {0.02459016393442623}^{1} = 122 \cdot 0.02459016393442623 = 3$

$a_{3} = a_{1} \cdot r^{n - 1} = 122 \cdot {0.02459016393442623}^{3 - 1} = 122 \cdot {0.02459016393442623}^{2} = 122 \cdot 0.0006046761623219564 = 0.07377049180327869$

$a_{4} = a_{1} \cdot r^{n - 1} = 122 \cdot {0.02459016393442623}^{4 - 1} = 122 \cdot {0.02459016393442623}^{3} = 122 \cdot 1.4869085958736634 E - 05 = 0.0018140284869658694$

$a_{5} = a_{1} \cdot r^{n - 1} = 122 \cdot {0.02459016393442623}^{5 - 1} = 122 \cdot {0.02459016393442623}^{4} = 122 \cdot 3.6563326128040904 E - 07 = 4.46072578762099 E - 05$

$a_{6} = a_{1} \cdot r^{n - 1} = 122 \cdot {0.02459016393442623}^{6 - 1} = 122 \cdot {0.02459016393442623}^{5} = 122 \cdot 8.990981834764156 E - 09 = 1.0968997838412272 E - 06$

$a_{7} = a_{1} \cdot r^{n - 1} = 122 \cdot {0.02459016393442623}^{7 - 1} = 122 \cdot {0.02459016393442623}^{6} = 122 \cdot 2.210897172482989 E - 10 = 2.6972945504292465 E - 08$

$a_{8} = a_{1} \cdot r^{n - 1} = 122 \cdot {0.02459016393442623}^{8 - 1} = 122 \cdot {0.02459016393442623}^{7} = 122 \cdot 5.4366323913516124 E - 12 = 6.632691517448967 E - 10$

$a_{9} = a_{1} \cdot r^{n - 1} = 122 \cdot {0.02459016393442623}^{9 - 1} = 122 \cdot {0.02459016393442623}^{8} = 122 \cdot 1.3368768175454784 E - 13 = 1.6309897174054836 E - 11$

$a_{10} = a_{1} \cdot r^{n - 1} = 122 \cdot {0.02459016393442623}^{10 - 1} = 122 \cdot {0.02459016393442623}^{9} = 122 \cdot 3.287402010357734 E - 15 = 4.0106304526364353 E - 13$

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几何数列