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解答 - 几何数列

公比是：

r = 0.12727272727272726

r=0.12727272727272726

该系列的和是：

s = 596750

s=596750

此系列的通用形式是：

a_{n} = 529375 \cdot {0.12727272727272726}^{n - 1}

a_n=529375*0.12727272727272726^(n-1)

这个序列的第n项是：

529375, 67375, 8574.999999999998, 1091.363636363636, 138.90082644628094, 17.678287002253935, 2.2499638002868645, 0.28635902912741906, 0.03644569461621697, 0.004638542951154886

529375,67375,8574.999999999998,1091.363636363636,138.90082644628094,17.678287002253935,2.2499638002868645,0.28635902912741906,0.03644569461621697,0.004638542951154886

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：

$a_{2} a_{1} = \frac{67375}{529375} = 0.12727272727272726$

该序列的公比（ $r$ ）保持不变，并且等于两个连续项的商。
$r = 0.12727272727272726$

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： $a = 529, 375$ 、公比： $r = 0.12727272727272726$ 和元素数目 $n = 2$ 插入几何级数求和公式：

$s_{2} = 529375 * ((1 - {0.12727272727272726}^{2}) / (1 - 0.12727272727272726))$

$s_{2} = 529375 * ((1 - 0.01619834710743801) / (1 - 0.12727272727272726))$

$s_{2} = 529375 * (0.9838016528925619 / (1 - 0.12727272727272726))$

$s_{2} = 529375 * (0.9838016528925619 / 0.8727272727272728)$

$s_{2} = 529375 \cdot 1.1272727272727272$

$s_{2} = 596750$

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： $a = 529, 375$ 和公比： $r = 0.12727272727272726$ 插入几何级数的公式：

$a_{n} = 529375 \cdot {0.12727272727272726}^{n - 1}$

4. 找到第n项

使用通用公式找到第n项

$a_{1} = 529375$

$a_{2} = a_{1} \cdot r^{n - 1} = 529375 \cdot {0.12727272727272726}^{2 - 1} = 529375 \cdot {0.12727272727272726}^{1} = 529375 \cdot 0.12727272727272726 = 67375$

$a_{3} = a_{1} \cdot r^{n - 1} = 529375 \cdot {0.12727272727272726}^{3 - 1} = 529375 \cdot {0.12727272727272726}^{2} = 529375 \cdot 0.01619834710743801 = 8574.999999999998$

$a_{4} = a_{1} \cdot r^{n - 1} = 529375 \cdot {0.12727272727272726}^{4 - 1} = 529375 \cdot {0.12727272727272726}^{3} = 529375 \cdot 0.0020616078136739286 = 1091.363636363636$

$a_{5} = a_{1} \cdot r^{n - 1} = 529375 \cdot {0.12727272727272726}^{5 - 1} = 529375 \cdot {0.12727272727272726}^{4} = 529375 \cdot 0.00026238644901304547 = 138.90082644628094$

$a_{6} = a_{1} \cdot r^{n - 1} = 529375 \cdot {0.12727272727272726}^{6 - 1} = 529375 \cdot {0.12727272727272726}^{5} = 529375 \cdot 3.339463896529669 E - 05 = 17.678287002253935$

$a_{7} = a_{1} \cdot r^{n - 1} = 529375 \cdot {0.12727272727272726}^{7 - 1} = 529375 \cdot {0.12727272727272726}^{6} = 529375 \cdot 4.250226777401397 E - 06 = 2.2499638002868645$

$a_{8} = a_{1} \cdot r^{n - 1} = 529375 \cdot {0.12727272727272726}^{8 - 1} = 529375 \cdot {0.12727272727272726}^{7} = 529375 \cdot 5.409379534874504 E - 07 = 0.28635902912741906$

$a_{9} = a_{1} \cdot r^{n - 1} = 529375 \cdot {0.12727272727272726}^{9 - 1} = 529375 \cdot {0.12727272727272726}^{8} = 529375 \cdot 6.88466486256755 E - 08 = 0.03644569461621697$

$a_{10} = a_{1} \cdot r^{n - 1} = 529375 \cdot {0.12727272727272726}^{10 - 1} = 529375 \cdot {0.12727272727272726}^{9} = 529375 \cdot 8.76230073417688 E - 09 = 0.004638542951154886$

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几何数列