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解答 - 几何数列

公比是：

r = 0.016150383902568177

r=0.016150383902568177

该系列的和是：

s = 7675

s=7675

此系列的通用形式是：

a_{n} = 7554 \cdot {0.016150383902568177}^{n - 1}

a_n=7554*0.016150383902568177^(n-1)

这个序列的第n项是：

7554, 122.00000000000001, 1.9703468361133178, 0.031821857824440664, 0.0005139352203576597, 8.300251109827176 E - 06, 1.3405224191142647 E - 07, 2.164995169869477 E - 09, 3.4965503140597865 E - 11, 5.647062990671088 E - 13

7554,122.00000000000001,1.9703468361133178,0.031821857824440664,0.0005139352203576597,8.300251109827176E-06,1.3405224191142647E-07,2.164995169869477E-09,3.4965503140597865E-11,5.647062990671088E-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：

$a_{2} a_{1} = \frac{122}{7554} = 0.016150383902568177$

该序列的公比（ $r$ ）保持不变，并且等于两个连续项的商。
$r = 0.016150383902568177$

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： $a = 7, 554$ 、公比： $r = 0.016150383902568177$ 和元素数目 $n = 2$ 插入几何级数求和公式：

$s_{2} = 7554 * ((1 - {0.016150383902568177}^{2}) / (1 - 0.016150383902568177))$

$s_{2} = 7554 * ((1 - 0.0002608349002003333) / (1 - 0.016150383902568177))$

$s_{2} = 7554 * (0.9997391650997997 / (1 - 0.016150383902568177))$

$s_{2} = 7554 * (0.9997391650997997 / 0.9838496160974318)$

$s_{2} = 7554 \cdot 1.016150383902568$

$s_{2} = 7675.999999999999$

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： $a = 7, 554$ 和公比： $r = 0.016150383902568177$ 插入几何级数的公式：

$a_{n} = 7554 \cdot {0.016150383902568177}^{n - 1}$

4. 找到第n项

使用通用公式找到第n项

$a_{1} = 7554$

$a_{2} = a_{1} \cdot r^{n - 1} = 7554 \cdot {0.016150383902568177}^{2 - 1} = 7554 \cdot {0.016150383902568177}^{1} = 7554 \cdot 0.016150383902568177 = 122.00000000000001$

$a_{3} = a_{1} \cdot r^{n - 1} = 7554 \cdot {0.016150383902568177}^{3 - 1} = 7554 \cdot {0.016150383902568177}^{2} = 7554 \cdot 0.0002608349002003333 = 1.9703468361133178$

$a_{4} = a_{1} \cdot r^{n - 1} = 7554 \cdot {0.016150383902568177}^{4 - 1} = 7554 \cdot {0.016150383902568177}^{3} = 7554 \cdot 4.21258377342344 E - 06 = 0.031821857824440664$

$a_{5} = a_{1} \cdot r^{n - 1} = 7554 \cdot {0.016150383902568177}^{5 - 1} = 7554 \cdot {0.016150383902568177}^{4} = 7554 \cdot 6.803484516251784 E - 08 = 0.0005139352203576597$

$a_{6} = a_{1} \cdot r^{n - 1} = 7554 \cdot {0.016150383902568177}^{6 - 1} = 7554 \cdot {0.016150383902568177}^{5} = 7554 \cdot 1.0987888681264465 E - 09 = 8.300251109827176 E - 06$

$a_{7} = a_{1} \cdot r^{n - 1} = 7554 \cdot {0.016150383902568177}^{7 - 1} = 7554 \cdot {0.016150383902568177}^{6} = 7554 \cdot 1.7745862048110468 E - 11 = 1.3405224191142647 E - 07$

$a_{8} = a_{1} \cdot r^{n - 1} = 7554 \cdot {0.016150383902568177}^{8 - 1} = 7554 \cdot {0.016150383902568177}^{7} = 7554 \cdot 2.8660248475899884 E - 13 = 2.164995169869477 E - 09$

$a_{9} = a_{1} \cdot r^{n - 1} = 7554 \cdot {0.016150383902568177}^{9 - 1} = 7554 \cdot {0.016150383902568177}^{8} = 7554 \cdot 4.628740156287776 E - 15 = 3.4965503140597865 E - 11$

$a_{10} = a_{1} \cdot r^{n - 1} = 7554 \cdot {0.016150383902568177}^{10 - 1} = 7554 \cdot {0.016150383902568177}^{9} = 7554 \cdot 7.475593050928102 E - 17 = 5.647062990671088 E - 13$

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几何数列