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解答 - 几何数列

公比是：

r = 0.04005252790544977

r=0.04005252790544977

该系列的和是：

s = 1584

s=1584

此系列的通用形式是：

a_{n} = 1523 \cdot {0.04005252790544977}^{n - 1}

a_n=1523*0.04005252790544977^(n-1)

这个序列的第n项是：

1523, 61, 2.443204202232436, 0.09785650448862677, 0.003919400376760494, 0.00015698189296283003, 6.287521648544078 E - 06, 2.518311362844312 E - 07, 1.0086473613493305 E - 08, 4.0398876587202336 E - 10

1523,61,2.443204202232436,0.09785650448862677,0.003919400376760494,0.00015698189296283003,6.287521648544078E-06,2.518311362844312E-07,1.0086473613493305E-08,4.0398876587202336E-10

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：

$a_{2} a_{1} = \frac{61}{1523} = 0.04005252790544977$

该序列的公比（ $r$ ）保持不变，并且等于两个连续项的商。
$r = 0.04005252790544977$

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： $a = 1, 523$ 、公比： $r = 0.04005252790544977$ 和元素数目 $n = 2$ 插入几何级数求和公式：

$s_{2} = 1523 * ((1 - {0.04005252790544977}^{2}) / (1 - 0.04005252790544977))$

$s_{2} = 1523 * ((1 - 0.0016042049916168324) / (1 - 0.04005252790544977))$

$s_{2} = 1523 * (0.9983957950083832 / (1 - 0.04005252790544977))$

$s_{2} = 1523 * (0.9983957950083832 / 0.9599474720945502)$

$s_{2} = 1523 \cdot 1.0400525279054498$

$s_{2} = 1584$

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： $a = 1, 523$ 和公比： $r = 0.04005252790544977$ 插入几何级数的公式：

$a_{n} = 1523 \cdot {0.04005252790544977}^{n - 1}$

4. 找到第n项

使用通用公式找到第n项

$a_{1} = 1523$

$a_{2} = a_{1} \cdot r^{n - 1} = 1523 \cdot {0.04005252790544977}^{2 - 1} = 1523 \cdot {0.04005252790544977}^{1} = 1523 \cdot 0.04005252790544977 = 61$

$a_{3} = a_{1} \cdot r^{n - 1} = 1523 \cdot {0.04005252790544977}^{3 - 1} = 1523 \cdot {0.04005252790544977}^{2} = 1523 \cdot 0.0016042049916168324 = 2.443204202232436$

$a_{4} = a_{1} \cdot r^{n - 1} = 1523 \cdot {0.04005252790544977}^{4 - 1} = 1523 \cdot {0.04005252790544977}^{3} = 1523 \cdot 6.425246519279499 E - 05 = 0.09785650448862677$

$a_{5} = a_{1} \cdot r^{n - 1} = 1523 \cdot {0.04005252790544977}^{5 - 1} = 1523 \cdot {0.04005252790544977}^{4} = 1523 \cdot 2.5734736551283613 E - 06 = 0.003919400376760494$

$a_{6} = a_{1} \cdot r^{n - 1} = 1523 \cdot {0.04005252790544977}^{6 - 1} = 1523 \cdot {0.04005252790544977}^{5} = 1523 \cdot 1.030741253859685 E - 07 = 0.00015698189296283003$

$a_{7} = a_{1} \cdot r^{n - 1} = 1523 \cdot {0.04005252790544977}^{7 - 1} = 1523 \cdot {0.04005252790544977}^{6} = 1523 \cdot 4.128379283351332 E - 09 = 6.287521648544078 E - 06$

$a_{8} = a_{1} \cdot r^{n - 1} = 1523 \cdot {0.04005252790544977}^{8 - 1} = 1523 \cdot {0.04005252790544977}^{7} = 1523 \cdot 1.6535202645070993 E - 10 = 2.518311362844312 E - 07$

$a_{9} = a_{1} \cdot r^{n - 1} = 1523 \cdot {0.04005252790544977}^{9 - 1} = 1523 \cdot {0.04005252790544977}^{8} = 1523 \cdot 6.622766653639728 E - 12 = 1.0086473613493305 E - 08$

$a_{10} = a_{1} \cdot r^{n - 1} = 1523 \cdot {0.04005252790544977}^{10 - 1} = 1523 \cdot {0.04005252790544977}^{9} = 1523 \cdot 2.6525854620618736 E - 13 = 4.0398876587202336 E - 10$

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几何数列