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解答 - 几何数列

公比是：

r = 0.23636363636363636

r=0.23636363636363636

该系列的和是：

s = 136

s=136

此系列的通用形式是：

a_{n} = 110 \cdot {0.23636363636363636}^{n - 1}

a_n=110*0.23636363636363636^(n-1)

这个序列的第n项是：

110, 26, 6.1454545454545455, 1.4525619834710743, 0.34333283245679935, 0.08115139676251622, 0.01918123923477656, 0.004533747455492641, 0.0010716130349346243, 0.0002532903537118203

110,26,6.1454545454545455,1.4525619834710743,0.34333283245679935,0.08115139676251622,0.01918123923477656,0.004533747455492641,0.0010716130349346243,0.0002532903537118203

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：

$a_{2} a_{1} = \frac{26}{110} = 0.23636363636363636$

该序列的公比（ $r$ ）保持不变，并且等于两个连续项的商。
$r = 0.23636363636363636$

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： $a = 110$ 、公比： $r = 0.23636363636363636$ 和元素数目 $n = 2$ 插入几何级数求和公式：

$s_{2} = 110 * ((1 - {0.23636363636363636}^{2}) / (1 - 0.23636363636363636))$

$s_{2} = 110 * ((1 - 0.05586776859504132) / (1 - 0.23636363636363636))$

$s_{2} = 110 * (0.9441322314049587 / (1 - 0.23636363636363636))$

$s_{2} = 110 * (0.9441322314049587 / 0.7636363636363637)$

$s_{2} = 110 \cdot 1.2363636363636363$

$s_{2} = 136$

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： $a = 110$ 和公比： $r = 0.23636363636363636$ 插入几何级数的公式：

$a_{n} = 110 \cdot {0.23636363636363636}^{n - 1}$

4. 找到第n项

使用通用公式找到第n项

$a_{1} = 110$

$a_{2} = a_{1} \cdot r^{n - 1} = 110 \cdot {0.23636363636363636}^{2 - 1} = 110 \cdot {0.23636363636363636}^{1} = 110 \cdot 0.23636363636363636 = 26$

$a_{3} = a_{1} \cdot r^{n - 1} = 110 \cdot {0.23636363636363636}^{3 - 1} = 110 \cdot {0.23636363636363636}^{2} = 110 \cdot 0.05586776859504132 = 6.1454545454545455$

$a_{4} = a_{1} \cdot r^{n - 1} = 110 \cdot {0.23636363636363636}^{4 - 1} = 110 \cdot {0.23636363636363636}^{3} = 110 \cdot 0.01320510894064613 = 1.4525619834710743$

$a_{5} = a_{1} \cdot r^{n - 1} = 110 \cdot {0.23636363636363636}^{5 - 1} = 110 \cdot {0.23636363636363636}^{4} = 110 \cdot 0.0031212075677890853 = 0.34333283245679935$

$a_{6} = a_{1} \cdot r^{n - 1} = 110 \cdot {0.23636363636363636}^{6 - 1} = 110 \cdot {0.23636363636363636}^{5} = 110 \cdot 0.0007377399705683292 = 0.08115139676251622$

$a_{7} = a_{1} \cdot r^{n - 1} = 110 \cdot {0.23636363636363636}^{7 - 1} = 110 \cdot {0.23636363636363636}^{6} = 110 \cdot 0.00017437490213433236 = 0.01918123923477656$

$a_{8} = a_{1} \cdot r^{n - 1} = 110 \cdot {0.23636363636363636}^{8 - 1} = 110 \cdot {0.23636363636363636}^{7} = 110 \cdot 4.121588595902401 E - 05 = 0.004533747455492641$

$a_{9} = a_{1} \cdot r^{n - 1} = 110 \cdot {0.23636363636363636}^{9 - 1} = 110 \cdot {0.23636363636363636}^{8} = 110 \cdot 9.741936681223857 E - 06 = 0.0010716130349346243$

$a_{10} = a_{1} \cdot r^{n - 1} = 110 \cdot {0.23636363636363636}^{10 - 1} = 110 \cdot {0.23636363636363636}^{9} = 110 \cdot 2.302639579198366 E - 06 = 0.0002532903537118203$

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几何数列