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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 = 846

s=846

此系列的通用形式是：

a_{n} = 396 \cdot {1.1363636363636365}^{n - 1}

a_n=396*1.1363636363636365^(n-1)

这个序列的第n项是：

396, 450.00000000000006, 511.3636363636365, 581.0950413223143, 660.3352742299026, 750.3809934430712, 852.7056743671264, 968.9837208717347, 1101.1178646269714, 1251.2703007124676

396,450.00000000000006,511.3636363636365,581.0950413223143,660.3352742299026,750.3809934430712,852.7056743671264,968.9837208717347,1101.1178646269714,1251.2703007124676

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：

$a_{2} a_{1} = \frac{450}{396} = 1.1363636363636365$

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： $a = 396$ 、公比： $r = 1.1363636363636365$ 和元素数目 $n = 2$ 插入几何级数求和公式：

$s_{2} = 396 * ((1 - {1.1363636363636365}^{2}) / (1 - 1.1363636363636365))$

$s_{2} = 396 * ((1 - 1.291322314049587) / (1 - 1.1363636363636365))$

$s_{2} = 396 * (- 0.2913223140495871 / (1 - 1.1363636363636365))$

$s_{2} = 396 * (- 0.2913223140495871 / - 0.13636363636363646)$

$s_{2} = 396 \cdot 2.136363636363637$

$s_{2} = 846.0000000000003$

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： $a = 396$ 和公比： $r = 1.1363636363636365$ 插入几何级数的公式：

$a_{n} = 396 \cdot {1.1363636363636365}^{n - 1}$

4. 找到第n项

使用通用公式找到第n项

$a_{1} = 396$

$a_{2} = a_{1} \cdot r^{n - 1} = 396 \cdot {1.1363636363636365}^{2 - 1} = 396 \cdot {1.1363636363636365}^{1} = 396 \cdot 1.1363636363636365 = 450.00000000000006$

$a_{3} = a_{1} \cdot r^{n - 1} = 396 \cdot {1.1363636363636365}^{3 - 1} = 396 \cdot {1.1363636363636365}^{2} = 396 \cdot 1.291322314049587 = 511.3636363636365$

$a_{4} = a_{1} \cdot r^{n - 1} = 396 \cdot {1.1363636363636365}^{4 - 1} = 396 \cdot {1.1363636363636365}^{3} = 396 \cdot 1.4674117205108945 = 581.0950413223143$

$a_{5} = a_{1} \cdot r^{n - 1} = 396 \cdot {1.1363636363636365}^{5 - 1} = 396 \cdot {1.1363636363636365}^{4} = 396 \cdot 1.6675133187623803 = 660.3352742299026$

$a_{6} = a_{1} \cdot r^{n - 1} = 396 \cdot {1.1363636363636365}^{6 - 1} = 396 \cdot {1.1363636363636365}^{5} = 396 \cdot 1.8949014985936141 = 750.3809934430712$

$a_{7} = a_{1} \cdot r^{n - 1} = 396 \cdot {1.1363636363636365}^{7 - 1} = 396 \cdot {1.1363636363636365}^{6} = 396 \cdot 2.1532971574927435 = 852.7056743671264$

$a_{8} = a_{1} \cdot r^{n - 1} = 396 \cdot {1.1363636363636365}^{8 - 1} = 396 \cdot {1.1363636363636365}^{7} = 396 \cdot 2.446928588059936 = 968.9837208717347$

$a_{9} = a_{1} \cdot r^{n - 1} = 396 \cdot {1.1363636363636365}^{9 - 1} = 396 \cdot {1.1363636363636365}^{8} = 396 \cdot 2.7806006682499276 = 1101.1178646269714$

$a_{10} = a_{1} \cdot r^{n - 1} = 396 \cdot {1.1363636363636365}^{10 - 1} = 396 \cdot {1.1363636363636365}^{9} = 396 \cdot 3.1597734866476452 = 1251.2703007124676$

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几何数列