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解答 - 几何数列

公比是：

r = 1.1363636363636365

r=1.1363636363636365

该系列的和是：

s = 282

s=282

此系列的通用形式是：

a_{n} = 132 \cdot {1.1363636363636365}^{n - 1}

a_n=132*1.1363636363636365^(n-1)

这个序列的第n项是：

132, 150, 170.4545454545455, 193.69834710743808, 220.1117580766342, 250.12699781435705, 284.23522478904215, 322.99457362391155, 367.03928820899046, 417.0901002374892

132,150,170.4545454545455,193.69834710743808,220.1117580766342,250.12699781435705,284.23522478904215,322.99457362391155,367.03928820899046,417.0901002374892

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：

$a_{2} a_{1} = \frac{150}{132} = 1.1363636363636365$

该序列的公比（ $r$ ）保持不变，并且等于两个连续项的商。
$r = 1.1363636363636365$

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： $a = 132$ 、公比： $r = 1.1363636363636365$ 和元素数目 $n = 2$ 插入几何级数求和公式：

$s_{2} = 132 * ((1 - {1.1363636363636365}^{2}) / (1 - 1.1363636363636365))$

$s_{2} = 132 * ((1 - 1.291322314049587) / (1 - 1.1363636363636365))$

$s_{2} = 132 * (- 0.2913223140495871 / (1 - 1.1363636363636365))$

$s_{2} = 132 * (- 0.2913223140495871 / - 0.13636363636363646)$

$s_{2} = 132 \cdot 2.136363636363637$

$s_{2} = 282.0000000000001$

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： $a = 132$ 和公比： $r = 1.1363636363636365$ 插入几何级数的公式：

$a_{n} = 132 \cdot {1.1363636363636365}^{n - 1}$

4. 找到第n项

使用通用公式找到第n项

$a_{1} = 132$

$a_{2} = a_{1} \cdot r^{n - 1} = 132 \cdot {1.1363636363636365}^{2 - 1} = 132 \cdot {1.1363636363636365}^{1} = 132 \cdot 1.1363636363636365 = 150$

$a_{3} = a_{1} \cdot r^{n - 1} = 132 \cdot {1.1363636363636365}^{3 - 1} = 132 \cdot {1.1363636363636365}^{2} = 132 \cdot 1.291322314049587 = 170.4545454545455$

$a_{4} = a_{1} \cdot r^{n - 1} = 132 \cdot {1.1363636363636365}^{4 - 1} = 132 \cdot {1.1363636363636365}^{3} = 132 \cdot 1.4674117205108945 = 193.69834710743808$

$a_{5} = a_{1} \cdot r^{n - 1} = 132 \cdot {1.1363636363636365}^{5 - 1} = 132 \cdot {1.1363636363636365}^{4} = 132 \cdot 1.6675133187623803 = 220.1117580766342$

$a_{6} = a_{1} \cdot r^{n - 1} = 132 \cdot {1.1363636363636365}^{6 - 1} = 132 \cdot {1.1363636363636365}^{5} = 132 \cdot 1.8949014985936141 = 250.12699781435705$

$a_{7} = a_{1} \cdot r^{n - 1} = 132 \cdot {1.1363636363636365}^{7 - 1} = 132 \cdot {1.1363636363636365}^{6} = 132 \cdot 2.1532971574927435 = 284.23522478904215$

$a_{8} = a_{1} \cdot r^{n - 1} = 132 \cdot {1.1363636363636365}^{8 - 1} = 132 \cdot {1.1363636363636365}^{7} = 132 \cdot 2.446928588059936 = 322.99457362391155$

$a_{9} = a_{1} \cdot r^{n - 1} = 132 \cdot {1.1363636363636365}^{9 - 1} = 132 \cdot {1.1363636363636365}^{8} = 132 \cdot 2.7806006682499276 = 367.03928820899046$

$a_{10} = a_{1} \cdot r^{n - 1} = 132 \cdot {1.1363636363636365}^{10 - 1} = 132 \cdot {1.1363636363636365}^{9} = 132 \cdot 3.1597734866476452 = 417.0901002374892$

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