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解答 - 几何数列

公比是：

r = 67.03030303030303

r=67.03030303030303

该系列的和是：

s = 4490

s=4490

此系列的通用形式是：

a_{n} = 66 \cdot {67.03030303030303}^{n - 1}

a_n=66*67.03030303030303^(n-1)

这个序列的第n项是：

66, 4424, 296542.0606060606, 19877304.18365473, 1332381722.8558867, 89309950635.06732, 5986473054689.968, 401275102938612.4, 26897591748491228, 1.8029537256867453 E + 18

66,4424,296542.0606060606,19877304.18365473,1332381722.8558867,89309950635.06732,5986473054689.968,401275102938612.4,26897591748491228,1.8029537256867453E+18

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：

$a_{2} a_{1} = \frac{4424}{66} = 67.03030303030303$

该序列的公比（ $r$ ）保持不变，并且等于两个连续项的商。
$r = 67.03030303030303$

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： $a = 66$ 、公比： $r = 67.03030303030303$ 和元素数目 $n = 2$ 插入几何级数求和公式：

$s_{2} = 66 * ((1 - {67.03030303030303}^{2}) / (1 - 67.03030303030303))$

$s_{2} = 66 * ((1 - 4493.061524334252) / (1 - 67.03030303030303))$

$s_{2} = 66 * (- 4492.061524334252 / (1 - 67.03030303030303))$

$s_{2} = 66 * (- 4492.061524334252 / - 66.03030303030303)$

$s_{2} = 66 \cdot 68.03030303030303$

$s_{2} = 4490$

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： $a = 66$ 和公比： $r = 67.03030303030303$ 插入几何级数的公式：

$a_{n} = 66 \cdot {67.03030303030303}^{n - 1}$

4. 找到第n项

使用通用公式找到第n项

$a_{1} = 66$

$a_{2} = a_{1} \cdot r^{n - 1} = 66 \cdot {67.03030303030303}^{2 - 1} = 66 \cdot {67.03030303030303}^{1} = 66 \cdot 67.03030303030303 = 4424$

$a_{3} = a_{1} \cdot r^{n - 1} = 66 \cdot {67.03030303030303}^{3 - 1} = 66 \cdot {67.03030303030303}^{2} = 66 \cdot 4493.061524334252 = 296542.0606060606$

$a_{4} = a_{1} \cdot r^{n - 1} = 66 \cdot {67.03030303030303}^{4 - 1} = 66 \cdot {67.03030303030303}^{3} = 66 \cdot 301171.27550992015 = 19877304.18365473$

$a_{5} = a_{1} \cdot r^{n - 1} = 66 \cdot {67.03030303030303}^{5 - 1} = 66 \cdot {67.03030303030303}^{4} = 66 \cdot 20187601.86145283 = 1332381722.8558867$

$a_{6} = a_{1} \cdot r^{n - 1} = 66 \cdot {67.03030303030303}^{6 - 1} = 66 \cdot {67.03030303030303}^{5} = 66 \cdot 1353181070.2282927 = 89309950635.06732$

$a_{7} = a_{1} \cdot r^{n - 1} = 66 \cdot {67.03030303030303}^{7 - 1} = 66 \cdot {67.03030303030303}^{6} = 66 \cdot 90704137192.27223 = 5986473054689.968$

$a_{8} = a_{1} \cdot r^{n - 1} = 66 \cdot {67.03030303030303}^{8 - 1} = 66 \cdot {67.03030303030303}^{7} = 66 \cdot 6079925802100.1875 = 401275102938612.4$

$a_{9} = a_{1} \cdot r^{n - 1} = 66 \cdot {67.03030303030303}^{9 - 1} = 66 \cdot {67.03030303030303}^{8} = 66 \cdot 407539268916533.75 = 26897591748491228$

$a_{10} = a_{1} \cdot r^{n - 1} = 66 \cdot {67.03030303030303}^{10 - 1} = 66 \cdot {67.03030303030303}^{9} = 66 \cdot 27317480692223416 = 1.8029537256867453 E + 18$

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