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解答 - 几何数列

公比是：

r = 0.07241764857658897

r=0.07241764857658897

该系列的和是：

s = 12469

s=12469

此系列的通用形式是：

a_{n} = 11627 \cdot {0.07241764857658897}^{n - 1}

a_n=11627*0.07241764857658897^(n-1)

这个序列的第n项是：

11627, 842, 60.97566010148791, 4.415713924955089, 0.31977561923214803, 0.02315739841691482, 0.0016770043405041953, 0.00012144471099204718, 8.794740402107484 E - 06, 6.368944197621486 E - 07

11627,842,60.97566010148791,4.415713924955089,0.31977561923214803,0.02315739841691482,0.0016770043405041953,0.00012144471099204718,8.794740402107484E-06,6.368944197621486E-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：

$a_{2} a_{1} = \frac{842}{11627} = 0.07241764857658897$

该序列的公比（ $r$ ）保持不变，并且等于两个连续项的商。
$r = 0.07241764857658897$

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： $a = 11, 627$ 、公比： $r = 0.07241764857658897$ 和元素数目 $n = 2$ 插入几何级数求和公式：

$s_{2} = 11627 * ((1 - {0.07241764857658897}^{2}) / (1 - 0.07241764857658897))$

$s_{2} = 11627 * ((1 - 0.005244315825362339) / (1 - 0.07241764857658897))$

$s_{2} = 11627 * (0.9947556841746377 / (1 - 0.07241764857658897))$

$s_{2} = 11627 * (0.9947556841746377 / 0.9275823514234111)$

$s_{2} = 11627 \cdot 1.072417648576589$

$s_{2} = 12469.000000000002$

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： $a = 11, 627$ 和公比： $r = 0.07241764857658897$ 插入几何级数的公式：

$a_{n} = 11627 \cdot {0.07241764857658897}^{n - 1}$

4. 找到第n项

使用通用公式找到第n项

$a_{1} = 11627$

$a_{2} = a_{1} \cdot r^{n - 1} = 11627 \cdot {0.07241764857658897}^{2 - 1} = 11627 \cdot {0.07241764857658897}^{1} = 11627 \cdot 0.07241764857658897 = 842$

$a_{3} = a_{1} \cdot r^{n - 1} = 11627 \cdot {0.07241764857658897}^{3 - 1} = 11627 \cdot {0.07241764857658897}^{2} = 11627 \cdot 0.005244315825362339 = 60.97566010148791$

$a_{4} = a_{1} \cdot r^{n - 1} = 11627 \cdot {0.07241764857658897}^{4 - 1} = 11627 \cdot {0.07241764857658897}^{3} = 11627 \cdot 0.00037978102046573397 = 4.415713924955089$

$a_{5} = a_{1} \cdot r^{n - 1} = 11627 \cdot {0.07241764857658897}^{5 - 1} = 11627 \cdot {0.07241764857658897}^{4} = 11627 \cdot 2.7502848476145868 E - 05 = 0.31977561923214803$

$a_{6} = a_{1} \cdot r^{n - 1} = 11627 \cdot {0.07241764857658897}^{6 - 1} = 11627 \cdot {0.07241764857658897}^{5} = 11627 \cdot 1.991691615800707 E - 06 = 0.02315739841691482$

$a_{7} = a_{1} \cdot r^{n - 1} = 11627 \cdot {0.07241764857658897}^{7 - 1} = 11627 \cdot {0.07241764857658897}^{6} = 11627 \cdot 1.4423362350599427 E - 07 = 0.0016770043405041953$

$a_{8} = a_{1} \cdot r^{n - 1} = 11627 \cdot {0.07241764857658897}^{8 - 1} = 11627 \cdot {0.07241764857658897}^{7} = 11627 \cdot 1.0445059859985136 E - 08 = 0.00012144471099204718$

$a_{9} = a_{1} \cdot r^{n - 1} = 11627 \cdot {0.07241764857658897}^{9 - 1} = 11627 \cdot {0.07241764857658897}^{8} = 11627 \cdot 7.564066743018391 E - 10 = 8.794740402107484 E - 06$

$a_{10} = a_{1} \cdot r^{n - 1} = 11627 \cdot {0.07241764857658897}^{10 - 1} = 11627 \cdot {0.07241764857658897}^{9} = 11627 \cdot 5.477719272057698 E - 11 = 6.368944197621486 E - 07$

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几何数列